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