// 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": [{"rulesets": {}, "preamble": {"js": "", "css": ""}, "tags": [], "ungrouped_variables": ["a1", "a2", "a3", "a4", "b1", "b2", "b3", "b4", "c1", "c2", "c3", "c4", "c5", "a", "b", "d1", "d2", "d3", "d4"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "pickQuestions": 0, "name": ""}], "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>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"scripts": {}, "variableReplacements": [], "prompt": "<p>$\\log_\\var{a2}\\var{a3}+\\log_\\var{a2}x = \\var{a4}$</p>\n<p>$x=$[[0]]</p>", "variableReplacementStrategy": "originalfirst", "gaps": [{"correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "numberentry", "integerAnswer": true, "showPrecisionHint": false, "allowFractions": false, "variableReplacements": [], "minValue": "{a1}", "integerPartialCredit": 0, "showCorrectAnswer": true, "marks": 1, "maxValue": "{a1}"}], "showCorrectAnswer": true, "marks": 0, "type": "gapfill"}, {"scripts": {}, "variableReplacements": [], "prompt": "<p>$\\log_\\var{b1}(x+\\var{b4})-\\log_\\var{b1}\\var{b2} = \\var{b3}$</p>\n<p>$x=$[[0]]</p>", "variableReplacementStrategy": "originalfirst", "gaps": [{"correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "numberentry", "integerAnswer": true, "showPrecisionHint": false, "allowFractions": false, "variableReplacements": [], "minValue": "{b2}*({b1}^{b3})-{b4}", "integerPartialCredit": 0, "showCorrectAnswer": true, "marks": 1, "maxValue": "{b2}*({b1}^{b3})-{b4}"}], "showCorrectAnswer": true, "marks": 0, "type": "gapfill"}, {"scripts": {}, "variableReplacements": [], "prompt": "<p>$\\log_\\var{c1}\\var{c2}x-\\log_\\var{c1}(\\var{c3}x-\\var{c4}) = \\var{c5}$</p>\n<p>$x=$[[0]]</p>", "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "type": "numberentry", "correctAnswerFraction": true, "variableReplacementStrategy": "originalfirst", "marks": 1, "showCorrectAnswer": true, "minValue": "({c4}*({c1}^{c5}))/(({c3}*({c1}^{c5}))-{c2})", "scripts": {}, "showPrecisionHint": false, "maxValue": "({c4}*({c1}^{c5}))/(({c3}*({c1}^{c5}))-{c2})"}], "showCorrectAnswer": true, "marks": 0, "type": "gapfill"}, {"scripts": {}, "variableReplacements": [], "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>", "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "type": "numberentry", "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "marks": 1, "showCorrectAnswer": true, "minValue": "{a}", "scripts": {}, "showPrecisionHint": false, "maxValue": "{a}"}, {"allowFractions": false, "variableReplacements": [], "type": "numberentry", "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "marks": 1, "showCorrectAnswer": true, "minValue": "{b}", "scripts": {}, "showPrecisionHint": false, "maxValue": "{b}"}], "showCorrectAnswer": true, "marks": 0, "type": "gapfill"}], "showQuestionGroupNames": false, "statement": "<p>Solve these equations for x, give your answer as integer or fraction.</p>", "variables": {"d3": {"description": "", "group": "Ungrouped variables", "name": "d3", "definition": "a*b", "templateType": "anything"}, "d1": {"description": "", "group": "Ungrouped variables", "name": "d1", "definition": "random(2..6)", "templateType": "anything"}, "b1": {"description": "", "group": "Ungrouped variables", "name": "b1", "definition": "random(2..6)", "templateType": "anything"}, "c2": {"description": "", "group": "Ungrouped variables", "name": "c2", "definition": "random(2..19)", "templateType": "anything"}, "a": {"description": "", "group": "Ungrouped variables", "name": "a", "definition": "random(1..9)", "templateType": "anything"}, "c1": {"description": "", "group": "Ungrouped variables", "name": "c1", "definition": "random(2..5)", "templateType": "anything"}, "b": {"description": "", "group": "Ungrouped variables", "name": "b", "definition": "floor(3a/2)", "templateType": "anything"}, "b4": {"description": "", "group": "Ungrouped variables", "name": "b4", "definition": "random(1..19)", "templateType": "anything"}, "d2": {"description": "", "group": "Ungrouped variables", "name": "d2", "definition": "random(2..5)", "templateType": "anything"}, "b2": {"description": "", "group": "Ungrouped variables", "name": "b2", "definition": "random(2..9)", "templateType": "anything"}, "d4": {"description": "", "group": "Ungrouped variables", "name": "d4", "definition": "+a+b", "templateType": "anything"}, "a2": {"description": "", "group": "Ungrouped variables", "name": "a2", "definition": "random([4,6,8,10])", "templateType": "anything"}, "c5": {"description": "", "group": "Ungrouped variables", "name": "c5", "definition": "random(1..5)", "templateType": "anything"}, "c3": {"description": "", "group": "Ungrouped variables", "name": "c3", "definition": "random(2..9 except c2)", "templateType": "anything"}, "a3": {"description": "", "group": "Ungrouped variables", "name": "a3", "definition": "a2/2", "templateType": "anything"}, "c4": {"description": "", "group": "Ungrouped variables", "name": "c4", "definition": "random(2..9 except c3)", "templateType": "anything"}, "a1": {"description": "", "group": "Ungrouped variables", "name": "a1", "definition": "2a2^((a4)-1)", "templateType": "anything"}, "a4": {"description": "", "group": "Ungrouped variables", "name": "a4", "definition": "random(2..3 except a2 except a3)", "templateType": "anything"}, "b3": {"description": "", "group": "Ungrouped variables", "name": "b3", "definition": "random(2..5)", "templateType": "anything"}}, "metadata": {"description": "", "notes": "", "licence": "Creative Commons Attribution 4.0 International"}, "functions": {}, "name": "Solving Logarithms", "type": "question", "contributors": [{"name": "joshua boddy", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/557/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "joshua boddy", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/557/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}