// Numbas version: exam_results_page_options
{"name": "Marta's copy of Logs: addition to multiplication 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", "ans2", "list", "b1", "b2", "arg"], "name": "Marta's copy of Logs: addition to multiplication inside", "tags": ["laws", "log laws", "logarithms", "logs", "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;$\\log_b\\left(ac\\right)$ =&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(ac).\\]</p>\n<p>Notice, all the bases are the same. Also, notice how the multiplication inside the log is the same as addition outside the log.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "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": false, "variableReplacements": [], "maxValue": "{ans2}", "minValue": "{ans2}", "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(ac).\\]</p>\n<p>Notice, all the bases are the same. Also, notice how the multiplication inside the log is the same as addition outside the log.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "<p>$\\log_\\var{b1}(\\var{arg})+\\log_\\var{b2}(\\var{arg})$ is equal to&nbsp;</p>\n<p></p>", "matrix": ["0", 0, 0, 0, 0, "1"], "shuffleChoices": false, "marks": 0, "variableReplacements": [], "choices": ["<p>$\\log_{\\var{b1}}(\\var{2*arg})$</p>", "<p>$\\log_{\\var{b1}}(\\var{arg^2})$</p>", "<p>$\\log_{\\var{b2}}(\\var{arg^2})$</p>", "<p>$\\log_{\\var{b1+b2}}(\\var{arg^2})$</p>", "<p>$\\log_{\\var{b1*b2}}(\\var{arg^2})$</p>", "<p>None of the other options</p>"], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>You might be trying to use the log law</p>\n<p>\\[\\log_b(a)+\\log_b(c)=\\log_b(ac).\\]</p>\n<p>but notice that we need all the bases to be the same.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "maxMarks": 0, "scripts": {}, "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."], "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "displayType": "radiogroup", "minMarks": 0}], "statement": "<p>Based on the definition of logarithms, determine the following:</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"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": ""}, "ans2": {"definition": "n1*n2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "list": {"definition": "reverse(sort(shuffle([2,3,4,5,10])[0..2]))", "templateType": "anything", "group": "Ungrouped variables", "name": "list", "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..12)", "templateType": "anything", "group": "Ungrouped variables", "name": "arg", "description": ""}, "n1": {"definition": "random(2..12)", "templateType": "anything", "group": "Ungrouped variables", "name": "n1", "description": ""}, "n2": {"definition": "random(2..12 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": "Marta S", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/782/"}]}]}], "contributors": [{"name": "Marta S", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/782/"}]}