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