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