// Numbas version: finer_feedback_settings
{"name": "Logs: subtraction to division inside", "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": ["laws", "log laws", "logarithms", "logs", "rules"], "ungrouped_variables": ["num1", "num2", "ans1", "n1", "n2", "m1", "m2", "m3", "arg", "list", "b1", "b2"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "pickQuestions": 0, "name": ""}], "advice": "", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"scripts": {}, "variableReplacements": [], "prompt": "<p>Suppose $\\log_b\\left(a\\right)=\\var{num1}$ and $\\log_b\\left(c\\right)=\\var{num2}$. Evaluate&nbsp;$\\log_b\\left(\\frac{a}{c}\\right)$ =&nbsp;[[0]].</p>", "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "type": "numberentry", "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "marks": 1, "showCorrectAnswer": true, "minValue": "{ans1}", "scripts": {}, "showPrecisionHint": false, "maxValue": "{ans1}"}], "showCorrectAnswer": true, "marks": 0, "type": "gapfill", "steps": [{"scripts": {}, "variableReplacements": [], "prompt": "<p>Here we are using the following log law</p>\n<p>\\[\\log_b(a)-\\log_b(c)=\\log_b\\left(\\frac{a}{c}\\right).\\]</p>\n<p>Notice, all the bases are the same. Also, notice how division inside the log becomes subtraction outside the log.&nbsp;</p>", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "marks": 0, "type": "information"}]}, {"scripts": {}, "variableReplacements": [], "prompt": "<p>$\\log_b(\\var{n1})-\\log_b(\\var{n2})$&nbsp;is equivalent to&nbsp;$\\log_b\\large($[[0]]$\\large)$.</p>", "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "type": "numberentry", "correctAnswerFraction": true, "variableReplacementStrategy": "originalfirst", "marks": 1, "showCorrectAnswer": true, "minValue": "{n1}/{n2}", "scripts": {}, "showPrecisionHint": false, "maxValue": "{n1}/{n2}"}], "showCorrectAnswer": true, "marks": 0, "type": "gapfill", "steps": [{"scripts": {}, "variableReplacements": [], "prompt": "<p>Here we are using the following log law</p>\n<p>\\[\\log_b(a)-\\log_b(c)=\\log_b\\left(\\frac{a}{c}\\right).\\]</p>\n<p>Notice, all the bases are the same. Also, notice how division inside the log becomes subtraction outside the log.&nbsp;</p>", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "marks": 0, "type": "information"}]}, {"scripts": {}, "variableReplacements": [], "prompt": "<p>$\\log_b(\\var{m1})-\\log_b(\\var{m2})+\\log_b(\\var{m3})$&nbsp;is equivalent to&nbsp;$\\log_b\\large($[[0]]$\\large)$.</p>", "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "type": "numberentry", "correctAnswerFraction": true, "variableReplacementStrategy": "originalfirst", "marks": 1, "showCorrectAnswer": true, "minValue": "{m1*m3}/{m2}", "scripts": {}, "showPrecisionHint": false, "maxValue": "{m1*m3}/{m2}"}], "showCorrectAnswer": true, "marks": 0, "type": "gapfill", "steps": [{"scripts": {}, "variableReplacements": [], "prompt": "<p><strong></strong>Here we are using the following log laws</p>\n<p>\\[\\log_b(a)-\\log_b(c)=\\log_b\\left(\\frac{a}{c}\\right).\\]</p>\n<p>\\[\\log_b(a)+\\log_b(c)=\\log_b(ac)\\]</p>\n<p>Notice, all the bases are the same.&nbsp;</p>", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "marks": 0, "type": "information"}]}, {"prompt": "<p>$\\log_\\var{b1}(\\var{10*arg})-\\log_\\var{b2}(\\var{arg})$ is equal to&nbsp;</p>\n<p></p>", "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "type": "1_n_2", "distractors": ["Log laws require the same base", "Log laws require the same base", "Log laws require the same base", "Log laws require the same base", "Log laws require the same base", "Log laws require the same base."], "steps": [{"scripts": {}, "variableReplacements": [], "prompt": "<p>Here we are using the following log law</p>\n<p>\\[\\log_b(a)-\\log_b(c)=\\log_b\\left(\\frac{a}{c}\\right).\\]</p>\n<p>Notice, all the bases are the same. Also, notice how division inside the log becomes subtraction outside the log.&nbsp;</p>", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "marks": 0, "type": "information"}], "variableReplacements": [], "shuffleChoices": false, "minMarks": 0, "scripts": {}, "maxMarks": 0, "showCorrectAnswer": true, "marks": 0, "displayColumns": 0, "choices": ["<p>$\\log_{\\var{b1}}(10)$</p>", "<p>$\\log_{\\var{b2}}(10)$</p>", "<p>$\\log_{\\var{b1*b2}}(10)$</p>", "<p>$\\log_{\\var{b1+b2}}(10)$</p>", "<p>$\\log_{\\var{b1-b2}}(10)$</p>", "<p>None of the other options&nbsp;</p>"], "matrix": [0, 0, 0, 0, 0, "1"], "displayType": "radiogroup"}], "showQuestionGroupNames": false, "statement": "<p>Based on the definition of logarithms, determine the following:</p>", "variables": {"n2": {"description": "", "group": "Ungrouped variables", "name": "n2", "definition": "random([2,3,5,7,11,13,17,19,23] except n1)", "templateType": "anything"}, "b1": {"description": "", "group": "Ungrouped variables", "name": "b1", "definition": "list[0]", "templateType": "anything"}, "num1": {"description": "", "group": "Ungrouped variables", "name": "num1", "definition": "random(-12..12 except [-1,0,1])", "templateType": "anything"}, "arg": {"description": "", "group": "Ungrouped variables", "name": "arg", "definition": "random(2..20)", "templateType": "anything"}, "m2": {"description": "", "group": "Ungrouped variables", "name": "m2", "definition": "random(2..12 except m1)", "templateType": "anything"}, "b2": {"description": "", "group": "Ungrouped variables", "name": "b2", "definition": "list[1]", "templateType": "anything"}, "ans1": {"description": "", "group": "Ungrouped variables", "name": "ans1", "definition": "num1-num2", "templateType": "anything"}, "m1": {"description": "", "group": "Ungrouped variables", "name": "m1", "definition": "random(2..12)", "templateType": "anything"}, "m3": {"description": "", "group": "Ungrouped variables", "name": "m3", "definition": "random(2..12 except [m1,m2])", "templateType": "anything"}, "num2": {"description": "", "group": "Ungrouped variables", "name": "num2", "definition": "random(-12..12 except [-1,0,1,num1])", "templateType": "anything"}, "n1": {"description": "", "group": "Ungrouped variables", "name": "n1", "definition": "random([2,3,5,7,11,13,17,19,23])", "templateType": "anything"}, "list": {"description": "", "group": "Ungrouped variables", "name": "list", "definition": "reverse(sort(shuffle([2,3,4,5,10])[0..2]))", "templateType": "anything"}}, "metadata": {"description": "", "notes": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "functions": {}, "name": "Logs: subtraction to division inside", "type": "question", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}