// Numbas version: exam_results_page_options
{"name": "Harry's copy of David'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": [{"tags": ["laws", "log laws", "logarithms", "Logarithms", "Logs", "logs", "rules"], "statement": "<p>Based on the definition of logarithms, determine the following:</p>", "advice": "", "parts": [{"scripts": {}, "type": "gapfill", "marks": 0, "variableReplacementStrategy": "originalfirst", "steps": [{"scripts": {}, "type": "information", "unitTests": [], "showFeedbackIcon": true, "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>", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showCorrectAnswer": true, "marks": 0}], "showCorrectAnswer": true, "unitTests": [], "stepsPenalty": "1", "customMarkingAlgorithm": "", "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>", "extendBaseMarkingAlgorithm": true, "gaps": [{"scripts": {}, "type": "numberentry", "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "minValue": "{ans1}", "mustBeReduced": false, "mustBeReducedPC": 0, "unitTests": [], "showFeedbackIcon": true, "variableReplacements": [], "customMarkingAlgorithm": "", "correctAnswerFraction": false, "maxValue": "{ans1}", "extendBaseMarkingAlgorithm": true, "marks": 1}], "variableReplacements": [], "sortAnswers": false, "showFeedbackIcon": true}, {"scripts": {}, "type": "gapfill", "marks": 0, "variableReplacementStrategy": "originalfirst", "steps": [{"scripts": {}, "type": "information", "unitTests": [], "showFeedbackIcon": true, "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>", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showCorrectAnswer": true, "marks": 0}], "showCorrectAnswer": true, "unitTests": [], "stepsPenalty": "1", "customMarkingAlgorithm": "", "prompt": "<p>$\\log_b(\\var{n1})+\\log_b(\\var{n2})$&nbsp;is equivalent to&nbsp;$\\log_b\\large($[[0]]$\\large)$.</p>", "extendBaseMarkingAlgorithm": true, "gaps": [{"scripts": {}, "type": "numberentry", "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "minValue": "{ans2}", "mustBeReduced": false, "mustBeReducedPC": 0, "unitTests": [], "showFeedbackIcon": true, "variableReplacements": [], "customMarkingAlgorithm": "", "correctAnswerFraction": false, "maxValue": "{ans2}", "extendBaseMarkingAlgorithm": true, "marks": 1}], "variableReplacements": [], "sortAnswers": false, "showFeedbackIcon": true}, {"scripts": {}, "matrix": ["0", 0, 0, 0, 0, "1"], "type": "1_n_2", "displayColumns": 0, "minMarks": 0, "maxMarks": 0, "variableReplacementStrategy": "originalfirst", "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>"], "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."], "shuffleChoices": false, "showCorrectAnswer": true, "steps": [{"scripts": {}, "type": "information", "unitTests": [], "showFeedbackIcon": true, "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>", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showCorrectAnswer": true, "marks": 0}], "unitTests": [], "showFeedbackIcon": true, "customMarkingAlgorithm": "", "prompt": "<p>$\\log_\\var{b1}(\\var{arg})+\\log_\\var{b2}(\\var{arg})$ is equal to&nbsp;</p>\n<p></p>", "extendBaseMarkingAlgorithm": true, "marks": 0, "variableReplacements": [], "displayType": "radiogroup", "stepsPenalty": "1"}], "ungrouped_variables": ["num1", "num2", "ans1", "n1", "n2", "ans2", "list", "b1", "b2", "arg"], "rulesets": {}, "functions": {}, "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "preamble": {"css": "", "js": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "variable_groups": [], "extensions": [], "variables": {"ans1": {"templateType": "anything", "definition": "num1+num2", "description": "", "group": "Ungrouped variables", "name": "ans1"}, "b1": {"templateType": "anything", "definition": "list[0]", "description": "", "group": "Ungrouped variables", "name": "b1"}, "num1": {"templateType": "anything", "definition": "random(-12..12 except [-1,0,1])", "description": "", "group": "Ungrouped variables", "name": "num1"}, "n2": {"templateType": "anything", "definition": "random(2..12 except n1)", "description": "", "group": "Ungrouped variables", "name": "n2"}, "num2": {"templateType": "anything", "definition": "random(-12..12 except [-1,0,1,num1])", "description": "", "group": "Ungrouped variables", "name": "num2"}, "b2": {"templateType": "anything", "definition": "list[1]", "description": "", "group": "Ungrouped variables", "name": "b2"}, "ans2": {"templateType": "anything", "definition": "n1*n2", "description": "", "group": "Ungrouped variables", "name": "ans2"}, "n1": {"templateType": "anything", "definition": "random(2..12)", "description": "", "group": "Ungrouped variables", "name": "n1"}, "arg": {"templateType": "anything", "definition": "random(2..12)", "description": "", "group": "Ungrouped variables", "name": "arg"}, "list": {"templateType": "anything", "definition": "reverse(sort(shuffle([2,3,4,5,10])[0..2]))", "description": "", "group": "Ungrouped variables", "name": "list"}}, "name": "Harry's copy of David's copy of Logs: addition to multiplication inside", "type": "question", "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/"}]}