// Numbas version: exam_results_page_options
{"name": "Harry's copy of David's copy of 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": [{"preamble": {"js": "", "css": ""}, "question_groups": [{"questions": [], "pickingStrategy": "all-ordered", "name": "", "pickQuestions": 0}], "showQuestionGroupNames": false, "variablesTest": {"condition": "", "maxRuns": 100}, "variables": {"n2": {"definition": "random([2,3,5,7,11,13,17,19,23] except n1)", "group": "Ungrouped variables", "name": "n2", "description": "", "templateType": "anything"}, "m3": {"definition": "random(2..12 except [m1,m2])", "group": "Ungrouped variables", "name": "m3", "description": "", "templateType": "anything"}, "num2": {"definition": "random(-12..12 except [-1,0,1,num1])", "group": "Ungrouped variables", "name": "num2", "description": "", "templateType": "anything"}, "list": {"definition": "reverse(sort(shuffle([2,3,4,5,10])[0..2]))", "group": "Ungrouped variables", "name": "list", "description": "", "templateType": "anything"}, "num1": {"definition": "random(-12..12 except [-1,0,1])", "group": "Ungrouped variables", "name": "num1", "description": "", "templateType": "anything"}, "m2": {"definition": "random(2..12 except m1)", "group": "Ungrouped variables", "name": "m2", "description": "", "templateType": "anything"}, "m1": {"definition": "random(2..12)", "group": "Ungrouped variables", "name": "m1", "description": "", "templateType": "anything"}, "n1": {"definition": "random([2,3,5,7,11,13,17,19,23])", "group": "Ungrouped variables", "name": "n1", "description": "", "templateType": "anything"}, "arg": {"definition": "random(2..20)", "group": "Ungrouped variables", "name": "arg", "description": "", "templateType": "anything"}, "b2": {"definition": "list[1]", "group": "Ungrouped variables", "name": "b2", "description": "", "templateType": "anything"}, "ans1": {"definition": "num1-num2", "group": "Ungrouped variables", "name": "ans1", "description": "", "templateType": "anything"}, "b1": {"definition": "list[0]", "group": "Ungrouped variables", "name": "b1", "description": "", "templateType": "anything"}}, "variable_groups": [], "tags": ["laws", "log laws", "logarithms", "logs", "rules"], "functions": {}, "type": "question", "parts": [{"steps": [{"type": "information", "marks": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "scripts": {}, "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>", "showCorrectAnswer": true}], "type": "gapfill", "marks": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "stepsPenalty": "1", "scripts": {}, "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>", "gaps": [{"showPrecisionHint": false, "maxValue": "{ans1}", "type": "numberentry", "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "marks": 1, "allowFractions": false, "correctAnswerFraction": false, "minValue": "{ans1}", "showCorrectAnswer": true}], "showCorrectAnswer": true}, {"steps": [{"type": "information", "marks": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "scripts": {}, "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>", "showCorrectAnswer": true}], "type": "gapfill", "marks": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "stepsPenalty": "1", "scripts": {}, "prompt": "<p>$\\log_b(\\var{n1})-\\log_b(\\var{n2})$&nbsp;is equivalent to&nbsp;$\\log_b\\large($[[0]]$\\large)$.</p>", "gaps": [{"showPrecisionHint": false, "maxValue": "{n1}/{n2}", "type": "numberentry", "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "marks": 1, "allowFractions": true, "correctAnswerFraction": true, "minValue": "{n1}/{n2}", "showCorrectAnswer": true}], "showCorrectAnswer": true}, {"steps": [{"type": "information", "marks": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "scripts": {}, "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>", "showCorrectAnswer": true}], "type": "gapfill", "marks": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "stepsPenalty": "1", "scripts": {}, "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>", "gaps": [{"showPrecisionHint": false, "maxValue": "{m1*m3}/{m2}", "type": "numberentry", "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "marks": 1, "allowFractions": true, "correctAnswerFraction": true, "minValue": "{m1*m3}/{m2}", "showCorrectAnswer": true}], "showCorrectAnswer": true}, {"steps": [{"type": "information", "marks": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "scripts": {}, "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>", "showCorrectAnswer": true}], "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>"], "showCorrectAnswer": true, "marks": 0, "variableReplacements": [], "shuffleChoices": false, "displayType": "radiogroup", "prompt": "<p>$\\log_\\var{b1}(\\var{10*arg})-\\log_\\var{b2}(\\var{arg})$ is equal to&nbsp;</p>\n<p></p>", "matrix": [0, 0, 0, 0, 0, "1"], "type": "1_n_2", "scripts": {}, "minMarks": 0, "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."], "variableReplacementStrategy": "originalfirst", "stepsPenalty": "1", "displayColumns": 0, "maxMarks": 0}], "name": "Harry's copy of David's copy of Logs: subtraction to division inside", "ungrouped_variables": ["num1", "num2", "ans1", "n1", "n2", "m1", "m2", "m3", "arg", "list", "b1", "b2"], "statement": "<p>Based on the definition of logarithms, determine the following:</p>", "advice": "", "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "notes": "", "description": ""}, "rulesets": {}, "contributors": [{"name": "David Martin", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/130/"}, {"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Harry Flynn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/976/"}]}]}], "contributors": [{"name": "David Martin", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/130/"}, {"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Harry Flynn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/976/"}]}