// Numbas version: exam_results_page_options
{"name": "Solving Logarithms ", "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", "a3", "a4", "b1", "b2", "b3", "b4", "c1", "c2", "c3", "c4", "c5", "a", "b", "d1", "d2", "d3", "d4"], "name": "Solving Logarithms ", "tags": [], "advice": "<p>We want to solve for x. After simplifying, in each case we end up with $\\log_a{f(x)} = b$, so we raise both sides as a power of $a$ to get $a^{\\log_a{f(x)}} = a^b$ which simplifies (by laws of logarithms) to $f(x)=a^b$. We then solve for x accordingly.</p>\n<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>", "rulesets": {}, "parts": [{"prompt": "<p>$\\log_\\var{a2}\\var{a3}+\\log_\\var{a2}x = \\var{a4}$</p>\n<p>$x=$[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{a1}", "minValue": "{a1}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\log_\\var{b1}(x+\\var{b4})-\\log_\\var{b1}\\var{b2} = \\var{b3}$</p>\n<p>$x=$[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{b2}*({b1}^{b3})-{b4}", "minValue": "{b2}*({b1}^{b3})-{b4}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\log_\\var{c1}\\var{c2}x-\\log_\\var{c1}(\\var{c3}x-\\var{c4}) = \\var{c5}$</p>\n<p>$x=$[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "({c4}*({c1}^{c5}))/(({c3}*({c1}^{c5}))-{c2})", "minValue": "({c4}*({c1}^{c5}))/(({c3}*({c1}^{c5}))-{c2})", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\log_\\var{d1}\\simplify{{d1}^{d2}}x^2 = \\var{d2} + \\log_\\var{d1}(\\var{d4}x-\\var{d3})$</p>\n<p>Give answers in ascending order</p>\n<p>$x=$[[0]],[[1]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{a}", "minValue": "{a}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{b}", "minValue": "{b}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Solve these equations for x, give your answer as integer or fraction.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "b4": {"definition": "random(1..19)", "templateType": "anything", "group": "Ungrouped variables", "name": "b4", "description": ""}, "b": {"definition": "floor(3a/2)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d1": {"definition": "random(2..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "d1", "description": ""}, "a1": {"definition": "2a2^((a4)-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "a3": {"definition": "a2/2", "templateType": "anything", "group": "Ungrouped variables", "name": "a3", "description": ""}, "a2": {"definition": "random([4,6,8,10])", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "c1": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "c1", "description": ""}, "b1": {"definition": "random(2..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}, "b2": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "b2", "description": ""}, "b3": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "b3", "description": ""}, "c3": {"definition": "random(2..9 except c2)", "templateType": "anything", "group": "Ungrouped variables", "name": "c3", "description": ""}, "c2": {"definition": "random(2..19)", "templateType": "anything", "group": "Ungrouped variables", "name": "c2", "description": ""}, "d4": {"definition": "+a+b", "templateType": "anything", "group": "Ungrouped variables", "name": "d4", "description": ""}, "c4": {"definition": "random(2..9 except c3)", "templateType": "anything", "group": "Ungrouped variables", "name": "c4", "description": ""}, "d2": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "d2", "description": ""}, "d3": {"definition": "a*b", "templateType": "anything", "group": "Ungrouped variables", "name": "d3", "description": ""}, "c5": {"definition": "random(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "c5", "description": ""}, "a4": {"definition": "random(2..3 except a2 except a3)", "templateType": "anything", "group": "Ungrouped variables", "name": "a4", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "joshua boddy", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/557/"}]}]}], "contributors": [{"name": "joshua boddy", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/557/"}]}