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