// Numbas version: exam_results_page_options
{"name": "Leonardo's copy of Logarithms", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"unitTests": [], "customName": "", "showCorrectAnswer": true, "variableReplacements": [], "customMarkingAlgorithm": "", "scripts": {}, "showFeedbackIcon": true, "marks": 0, "gaps": [{"unitTests": [], "customName": "", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "minValue": "a1*a2", "showFeedbackIcon": false, "showFractionHint": true, "customMarkingAlgorithm": "", "scripts": {}, "allowFractions": false, "marks": 1, "correctAnswerStyle": "plain", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "type": "numberentry", "maxValue": "a1*a2", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "correctAnswerFraction": false, "variableReplacements": []}], "useCustomName": false, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "prompt": "<p>$\\log{\\var{a1}} + \\log{\\var{a2}} = \\log$[[0]]</p>", "extendBaseMarkingAlgorithm": true, "sortAnswers": false}, {"unitTests": [], "customName": "", "showCorrectAnswer": true, "variableReplacements": [], "customMarkingAlgorithm": "", "scripts": {}, "showFeedbackIcon": true, "marks": 0, "gaps": [{"unitTests": [], "customName": "", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "minValue": "b1*b2", "showFeedbackIcon": false, "showFractionHint": true, "customMarkingAlgorithm": "", "scripts": {}, "allowFractions": false, "marks": 1, "correctAnswerStyle": "plain", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "type": "numberentry", "maxValue": "b1*b2", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "correctAnswerFraction": false, "variableReplacements": []}], "useCustomName": false, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "prompt": "<p>$\\log{\\var{b1}} + \\log{\\var{b2}} = \\log$[[0]]</p>", "extendBaseMarkingAlgorithm": true, "sortAnswers": false}, {"unitTests": [], "customName": "", "showCorrectAnswer": true, "variableReplacements": [], "customMarkingAlgorithm": "", "scripts": {}, "showFeedbackIcon": true, "marks": 0, "gaps": [{"unitTests": [], "customName": "", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "minValue": "c1", "showFeedbackIcon": false, "showFractionHint": true, "customMarkingAlgorithm": "", "scripts": {}, "allowFractions": false, "marks": 1, "correctAnswerStyle": "plain", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "type": "numberentry", "maxValue": "c1", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "correctAnswerFraction": false, "variableReplacements": []}], "useCustomName": false, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "prompt": "<p>$\\log{\\var{c3}} - \\log{\\var{c2}} = \\log$[[0]]</p>", "extendBaseMarkingAlgorithm": true, "sortAnswers": false}, {"unitTests": [], "customName": "", "showCorrectAnswer": true, "variableReplacements": [], "customMarkingAlgorithm": "", "scripts": {}, "showFeedbackIcon": true, "marks": 0, "gaps": [{"unitTests": [], "customName": "", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "minValue": "e1*e2*e3", "showFeedbackIcon": false, "showFractionHint": true, "customMarkingAlgorithm": "", "scripts": {}, "allowFractions": false, "marks": 1, "correctAnswerStyle": "plain", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "type": "numberentry", "maxValue": "e1*e2*e3", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "correctAnswerFraction": false, "variableReplacements": []}], "useCustomName": false, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "prompt": "<p>$\\log{\\var{e1}} + \\log{\\var{e2}} + \\log{\\var{e3}} = \\log$[[0]]</p>", "extendBaseMarkingAlgorithm": true, "sortAnswers": false}, {"unitTests": [], "customName": "", "showCorrectAnswer": true, "variableReplacements": [], "customMarkingAlgorithm": "", "scripts": {}, "showFeedbackIcon": true, "marks": 0, "gaps": [{"unitTests": [], "customName": "", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "minValue": "f1*f3/f5", "showFeedbackIcon": false, "showFractionHint": true, "customMarkingAlgorithm": "", "scripts": {}, "allowFractions": false, "marks": 1, "correctAnswerStyle": "plain", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "type": "numberentry", "maxValue": "f1*f3/f5", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "correctAnswerFraction": false, "variableReplacements": []}], "useCustomName": false, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "prompt": "<p>$\\log{\\var{f1}} + \\log{\\var{f3}} - \\log{\\var{f5}} = \\log$[[0]]</p>", "extendBaseMarkingAlgorithm": true, "sortAnswers": false}, {"unitTests": [], "customName": "", "showCorrectAnswer": true, "variableReplacements": [], "customMarkingAlgorithm": "", "scripts": {}, "showFeedbackIcon": true, "marks": 0, "gaps": [{"unitTests": [], "customName": "", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "minValue": "g2^(g1-1)", "showFeedbackIcon": false, "showFractionHint": true, "customMarkingAlgorithm": "", "scripts": {}, "allowFractions": false, "marks": 1, "correctAnswerStyle": "plain", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "type": "numberentry", "maxValue": "g2^(g1-1)", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "correctAnswerFraction": false, "variableReplacements": []}], "useCustomName": false, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "prompt": "<p>$\\var{g1}\\log{\\var{g2}} + \\log{\\var{g3}} - \\log{\\var{g4}}=\\log$[[0]]</p>", "extendBaseMarkingAlgorithm": true, "sortAnswers": false}, {"unitTests": [], "customName": "", "showCorrectAnswer": true, "variableReplacements": [], "customMarkingAlgorithm": "", "scripts": {}, "showFeedbackIcon": true, "marks": 0, "gaps": [{"unitTests": [], "customName": "", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "minValue": "(h1)^0.5", "showFeedbackIcon": false, "showFractionHint": true, "customMarkingAlgorithm": "", "scripts": {}, "allowFractions": false, "marks": 1, "correctAnswerStyle": "plain", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "type": "numberentry", "maxValue": "(h1)^0.5", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "correctAnswerFraction": false, "variableReplacements": []}], "useCustomName": false, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "prompt": "<p>$\\frac{1}{2}\\log{\\var{h3}} - \\frac{1}{2}\\log{\\var{h2}}=\\log$[[0]]</p>", "extendBaseMarkingAlgorithm": true, "sortAnswers": false}, {"unitTests": [], "customName": "", "showCorrectAnswer": true, "variableReplacements": [], "customMarkingAlgorithm": "", "scripts": {}, "showFeedbackIcon": true, "marks": 0, "gaps": [{"unitTests": [], "customName": "", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "minValue": "i1", "showFeedbackIcon": false, "showFractionHint": true, "customMarkingAlgorithm": "", "scripts": {}, "allowFractions": false, "marks": 1, "correctAnswerStyle": "plain", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "type": "numberentry", "maxValue": "i1", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "correctAnswerFraction": false, "variableReplacements": []}], "useCustomName": false, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "prompt": "<p>$\\log{\\var{i3}}-\\frac{1}{2}\\log{\\var{i4}} = \\log$[[0]]</p>", "extendBaseMarkingAlgorithm": true, "sortAnswers": false}, {"unitTests": [], "customName": "", "showCorrectAnswer": true, "variableReplacements": [], "customMarkingAlgorithm": "", "scripts": {}, "showFeedbackIcon": true, "marks": 0, "gaps": [{"unitTests": [], "customName": "", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "minValue": "a1^2+ sqrt{4}{h4}", "showFeedbackIcon": false, "showFractionHint": true, "customMarkingAlgorithm": "", "scripts": {}, "allowFractions": false, "marks": 1, "correctAnswerStyle": "plain", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "type": "numberentry", "maxValue": "a1^2+ sqrt{4}{h4}", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "correctAnswerFraction": false, "variableReplacements": []}], "useCustomName": false, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "prompt": "<p>$\\frac{1}{4}\\log{\\var{h4}} + 2\\log{\\var{a1}}=\\log$[[0]]</p>", "extendBaseMarkingAlgorithm": true, "sortAnswers": false}, {"unitTests": [], "customName": "", "showCorrectAnswer": true, "variableReplacements": [], "customMarkingAlgorithm": "", "scripts": {}, "showFeedbackIcon": true, "marks": 0, "gaps": [{"unitTests": [], "customName": "", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "minValue": "1/g", "showFeedbackIcon": false, "showFractionHint": true, "customMarkingAlgorithm": "", "scripts": {}, "allowFractions": false, "marks": 1, "correctAnswerStyle": "plain", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "type": "numberentry", "maxValue": "1/g", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "correctAnswerFraction": false, "variableReplacements": []}], "useCustomName": false, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "prompt": "<p>$-\\log \\var{g}=\\log$[[0]]</p>", "extendBaseMarkingAlgorithm": true, "sortAnswers": false}, {"unitTests": [], "customName": "", "showCorrectAnswer": true, "variableReplacements": [], "customMarkingAlgorithm": "", "scripts": {}, "showFeedbackIcon": true, "marks": 0, "gaps": [{"unitTests": [], "customName": "", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "minValue": "81 b", "showFeedbackIcon": false, "showFractionHint": true, "customMarkingAlgorithm": "", "scripts": {}, "allowFractions": false, "marks": 1, "correctAnswerStyle": "plain", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "type": "numberentry", "maxValue": "81 b", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "correctAnswerFraction": false, "variableReplacements": []}], "useCustomName": false, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "prompt": "<p>$ \\log{\\var{a}} - 2\\log{\\var{b}}+ 3\\log{\\var{c}} - 4\\log{\\var{d}} =\\log$[[0]]</p>", "extendBaseMarkingAlgorithm": true, "sortAnswers": false}], "variable_groups": [], "statement": "<p>Express each of the following as a single logarithm</p>\n<p></p>", "extensions": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Practice using the log rules to add and subtract logarithms</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "variables": {"b": {"definition": "random([2,3,5,7,11]except jolly)", "name": "b", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "b1": {"definition": "random(2..19 except a2 except a1)", "name": "b1", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "e2": {"definition": "random(2..9 except e1)", "name": "e2", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "g1": {"definition": "random(2..4)", "name": "g1", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "h2": {"definition": "random([2,3,5,7,8,10])", "name": "h2", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "d3": {"definition": "d1*d2", "name": "d3", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "i4": {"definition": "i2^2", "name": "i4", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "h4": {"definition": "random(16,64,256,1024,4096,16384)", "name": "h4", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "f2": {"definition": "random(3..5 except f1)", "name": "f2", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "a1": {"definition": "random(2..9)", "name": "a1", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "i2": {"definition": "random(2..9)", "name": "i2", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "d1": {"definition": "random(2..19)", "name": "d1", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "h3": {"definition": "h1*h2", "name": "h3", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "d2": {"definition": "random(2..9 except d1)", "name": "d2", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "g2": {"definition": "random(2..9 except g1)", "name": "g2", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "a": {"definition": "(jolly)^4*3 ", "name": "a", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "f4": {"definition": "f2-1", "name": "f4", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "f3": {"definition": "f1*f2", "name": "f3", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "jolly": {"definition": "random(2,3,5,7,11,13,17,19,23)", "name": "jolly", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "g": {"definition": "random(2,4,5,8,10)", "name": "g", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "g3": {"definition": "random(2..9 except g2 except g1)", "name": "g3", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "i3": {"definition": "i1*i2", "name": "i3", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "g4": {"definition": "g2*g3", "name": "g4", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "f5": {"definition": "f1^2", "name": "f5", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "e1": {"definition": "random(2..9)", "name": "e1", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "c": {"definition": "(b*3)", "name": "c", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "b2": {"definition": "random(2..19 except a1 except a2 except b1)", "name": "b2", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "f1": {"definition": "random(2..9)", "name": "f1", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "h1": {"definition": "random([4,9,16,25])", "name": "h1", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "d": {"definition": "jolly", "name": "d", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "i1": {"definition": "random(2..9)", "name": "i1", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "c2": {"definition": "random(2..9 except c1)", "name": "c2", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "e3": {"definition": "random(2..9 except e1 except e2)", "name": "e3", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "c1": {"definition": "random(2..19)", "name": "c1", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "c3": {"definition": "c1*c2", "name": "c3", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "a2": {"definition": "random(2..9 except a1)", "name": "a2", "description": "", "templateType": "anything", "group": "Ungrouped variables"}}, "name": "Leonardo's copy of Logarithms", "rulesets": {}, "preamble": {"css": "", "js": ""}, "advice": "<p>Use of the laws of logarithms is crucial here:</p>\n<p>$\\log{a} + \\log{b} = \\log{ab}$</p>\n<p>$\\log{a} - \\log{b} = \\log{\\frac{a}{b}}$</p>\n<p>$\\log{a^n} = n\\log{a}$</p>\n<p></p>", "ungrouped_variables": ["a1", "a2", "b1", "b2", "c1", "c2", "c3", "d1", "d2", "d3", "e1", "e2", "e3", "f1", "f2", "f3", "f4", "f5", "g1", "g2", "g3", "g4", "h1", "h2", "h3", "h4", "i1", "i2", "i3", "i4", "g", "a", "b", "c", "d", "jolly"], "functions": {}, "tags": [], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "David Martin", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/130/"}, {"name": "Angharad Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/315/"}, {"name": "Leonardo Juliano", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3600/"}]}]}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "David Martin", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/130/"}, {"name": "Angharad Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/315/"}, {"name": "Leonardo Juliano", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3600/"}]}