// Numbas version: exam_results_page_options
{"name": "Adding and Subtracting Logs", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "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", "i1", "i2", "i3", "i4"], "name": "Adding and Subtracting Logs", "tags": ["Logarithm", "Logs", "rebel", "rebelmaths", "Rules of Logs"], "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>", "rulesets": {}, "parts": [{"prompt": "<p>$\\log{\\var{a1}} + \\log{\\var{a2}} = \\log$[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "a1*a2", "minValue": "a1*a2", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\log{\\var{b1}} + \\log{\\var{b2}} = \\log$[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "b1*b2", "minValue": "b1*b2", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\log{\\var{c3}} - \\log{\\var{c2}} = \\log$[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "c1", "minValue": "c1", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\log{\\var{e1}} + \\log{\\var{e2}} + \\log{\\var{e3}} = \\log$[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "e1*e2*e3", "minValue": "e1*e2*e3", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\log{\\var{f1}} + \\log{\\var{f3}} - \\log{\\var{f5}} = \\log$[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "f1*f3/f5", "minValue": "f1*f3/f5", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\var{g1}\\log{\\var{g2}} + \\log{\\var{g3}} - \\log{\\var{g4}}=\\log$[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "g2^(g1-1)", "minValue": "g2^(g1-1)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\frac{1}{2}\\log{\\var{h3}} - \\frac{1}{2}\\log{\\var{h2}}=\\log$[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "(h1)^0.5", "minValue": "(h1)^0.5", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\log{\\var{i3}}-\\frac{1}{2}\\log{\\var{i4}} = \\log$[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "i1", "minValue": "i1", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Express each of the following as a single logarithm</p>\n<p></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"f1": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "f1", "description": ""}, "f2": {"definition": "random(3..5 except f1)", "templateType": "anything", "group": "Ungrouped variables", "name": "f2", "description": ""}, "f3": {"definition": "f1*f2", "templateType": "anything", "group": "Ungrouped variables", "name": "f3", "description": ""}, "f4": {"definition": "f2-1", "templateType": "anything", "group": "Ungrouped variables", "name": "f4", "description": ""}, "f5": {"definition": "f1^2", "templateType": "anything", "group": "Ungrouped variables", "name": "f5", "description": ""}, "h2": {"definition": "random([2,3,5,7,8,10])", "templateType": "anything", "group": "Ungrouped variables", "name": "h2", "description": ""}, "h3": {"definition": "h1*h2", "templateType": "anything", "group": "Ungrouped variables", "name": "h3", "description": ""}, "h1": {"definition": "random([4,9,16,25])", "templateType": "anything", "group": "Ungrouped variables", "name": "h1", "description": ""}, "b1": {"definition": "random(2..19 except a2 except a1)", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}, "b2": {"definition": "random(2..19 except a1 except a2 except b1)", "templateType": "anything", "group": "Ungrouped variables", "name": "b2", "description": ""}, "d2": {"definition": "random(2..9 except d1)", "templateType": "anything", "group": "Ungrouped variables", "name": "d2", "description": ""}, "d3": {"definition": "d1*d2", "templateType": "anything", "group": "Ungrouped variables", "name": "d3", "description": ""}, "d1": {"definition": "random(2..19)", "templateType": "anything", "group": "Ungrouped variables", "name": "d1", "description": ""}, "g4": {"definition": "g2*g3", "templateType": "anything", "group": "Ungrouped variables", "name": "g4", "description": ""}, "g3": {"definition": "random(2..9 except g2 except g1)", "templateType": "anything", "group": "Ungrouped variables", "name": "g3", "description": ""}, "g2": {"definition": "random(2..9 except g1)", "templateType": "anything", "group": "Ungrouped variables", "name": "g2", "description": ""}, "g1": {"definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "g1", "description": ""}, "i1": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "i1", "description": ""}, "i3": {"definition": "i1*i2", "templateType": "anything", "group": "Ungrouped variables", "name": "i3", "description": ""}, "i2": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "i2", "description": ""}, "i4": {"definition": "i2^2", "templateType": "anything", "group": "Ungrouped variables", "name": "i4", "description": ""}, "a1": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "a2": {"definition": "random(2..9 except a1)", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "c3": {"definition": "c1*c2", "templateType": "anything", "group": "Ungrouped variables", "name": "c3", "description": ""}, "c2": {"definition": "random(2..9 except c1)", "templateType": "anything", "group": "Ungrouped variables", "name": "c2", "description": ""}, "c1": {"definition": "random(2..19)", "templateType": "anything", "group": "Ungrouped variables", "name": "c1", "description": ""}, "e1": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "e1", "description": ""}, "e3": {"definition": "random(2..9 except e1 except e2)", "templateType": "anything", "group": "Ungrouped variables", "name": "e3", "description": ""}, "e2": {"definition": "random(2..9 except e1)", "templateType": "anything", "group": "Ungrouped variables", "name": "e2", "description": ""}}, "metadata": {"notes": "<p>rebelmaths rebel Rebel REBEL</p>", "description": "<p>Practice using the log rules to add and subtract logarithms</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "steve kilgallon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/268/"}]}]}], "contributors": [{"name": "steve kilgallon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/268/"}]}