// Numbas version: exam_results_page_options
{"name": "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": [{"metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "variable_groups": [], "name": "Logs: addition to multiplication inside", "ungrouped_variables": ["num1", "num2", "ans1", "n1", "n2", "ans2", "list", "b1", "b2", "arg"], "functions": {}, "tags": ["laws", "log laws", "logarithms", "Logarithms", "Logs", "logs", "rules"], "variablesTest": {"condition": "", "maxRuns": 100}, "extensions": [], "variables": {"arg": {"name": "arg", "definition": "random(2..12)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "n2": {"name": "n2", "definition": "random(2..12 except n1)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "num2": {"name": "num2", "definition": "random(-12..12 except [-1,0,1,num1])", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "ans1": {"name": "ans1", "definition": "num1+num2", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "ans2": {"name": "ans2", "definition": "n1*n2", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "b1": {"name": "b1", "definition": "list[0]", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "n1": {"name": "n1", "definition": "random(2..12)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "num1": {"name": "num1", "definition": "random(-12..12 except [-1,0,1])", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "list": {"name": "list", "definition": "reverse(sort(shuffle([2,3,4,5,10])[0..2]))", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "b2": {"name": "b2", "definition": "list[1]", "group": "Ungrouped variables", "description": "", "templateType": "anything"}}, "statement": "<p>Based on the definition of logarithms, determine the following:</p>", "parts": [{"type": "gapfill", "customMarkingAlgorithm": "", "unitTests": [], "variableReplacementStrategy": "originalfirst", "marks": 0, "showFeedbackIcon": true, "gaps": [{"type": "numberentry", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "allowFractions": false, "maxValue": "{ans1}", "variableReplacementStrategy": "originalfirst", "marks": 1, "showFeedbackIcon": true, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "minValue": "{ans1}", "mustBeReduced": false, "unitTests": [], "variableReplacements": [], "correctAnswerFraction": false}], "sortAnswers": false, "steps": [{"type": "information", "customMarkingAlgorithm": "", "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "marks": 0, "showFeedbackIcon": true, "showCorrectAnswer": 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>", "unitTests": [], "variableReplacements": []}], "scripts": {}, "extendBaseMarkingAlgorithm": true, "stepsPenalty": "1", "showCorrectAnswer": true, "prompt": "<p>Suppose $\\log_b\\left(a\\right)=\\var{num1}$ and $\\log_b\\left(c\\right)=\\var{num2}$. Evaluate&nbsp;$\\log_b\\left(ac\\right)$ =&nbsp;[[0]].</p>", "variableReplacements": []}, {"type": "gapfill", "customMarkingAlgorithm": "", "unitTests": [], "variableReplacementStrategy": "originalfirst", "marks": 0, "showFeedbackIcon": true, "gaps": [{"type": "numberentry", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "allowFractions": false, "maxValue": "{ans2}", "variableReplacementStrategy": "originalfirst", "marks": 1, "showFeedbackIcon": true, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "minValue": "{ans2}", "mustBeReduced": false, "unitTests": [], "variableReplacements": [], "correctAnswerFraction": false}], "sortAnswers": false, "steps": [{"type": "information", "customMarkingAlgorithm": "", "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "marks": 0, "showFeedbackIcon": true, "showCorrectAnswer": 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>", "unitTests": [], "variableReplacements": []}], "scripts": {}, "extendBaseMarkingAlgorithm": true, "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>", "variableReplacements": []}, {"type": "1_n_2", "customMarkingAlgorithm": "", "maxMarks": 0, "unitTests": [], "variableReplacementStrategy": "originalfirst", "marks": 0, "showFeedbackIcon": true, "displayColumns": 0, "minMarks": 0, "variableReplacements": [], "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."], "steps": [{"type": "information", "customMarkingAlgorithm": "", "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "marks": 0, "showFeedbackIcon": true, "showCorrectAnswer": 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>", "unitTests": [], "variableReplacements": []}], "shuffleChoices": false, "scripts": {}, "extendBaseMarkingAlgorithm": true, "displayType": "radiogroup", "stepsPenalty": "1", "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>"], "showCorrectAnswer": true, "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"]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}