// Numbas version: exam_results_page_options
{"name": "David's copy of Logs: change of base", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"tags": ["change of base", "log laws", "logarithms", "logs", "rules"], "metadata": {"notes": "<p>Could make a questions on rewriting expressions involving logs in terms of a single log, and solving equations.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": ""}, "ungrouped_variables": ["base1", "arg1", "base2", "num", "den"], "parts": [{"steps": [{"variableReplacementStrategy": "originalfirst", "prompt": "<p>In this question we are using the change of base rule:</p>\n<p>\\[\\log_b(a)=\\frac{\\log_c(a)}{\\log_c(b)}\\]</p>\n<p>Notice, $c$ can be any base. Also, notice the big $a$ goes at the top of the fraction, and the little $b$ goes down the bottom.</p>", "variableReplacements": [], "marks": 0, "showCorrectAnswer": true, "scripts": {}, "type": "information"}], "prompt": "<p>$\\ln(x)$ is the natural logarithm of $x$, or the log of $x$ base $e$. This is equivalent to $\\log_e(x)$ but $\\ln(x)$ is normally preferred, in fact, for this question it is required.</p>\n<p>&nbsp;&nbsp;<br/>$\\log_{\\var{base1}}(\\var{arg1})$ can be written in terms of natural logarithms as&nbsp;[[0]].</p>", "variableReplacements": [], "stepsPenalty": "1", "marks": 0, "gaps": [{"checkvariablenames": false, "marks": 1, "answer": "(ln{arg1})/(ln{base1})", "type": "jme", "scripts": {}, "showpreview": true, "variableReplacements": [], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "vsetrangepoints": 5, "checkingaccuracy": 0.001, "expectedvariablenames": [], "vsetrange": ["0.1", "0.9"], "checkingtype": "absdiff"}], "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "gapfill", "showCorrectAnswer": true}, {"distractors": ["", "", "", "", ""], "prompt": "<p>The expression $\\displaystyle\\frac{\\log_\\var{base2}(\\var{num})}{\\log_\\var{base2}(\\var{den})}$ can be written as</p>", "stepsPenalty": "1", "marks": 0, "steps": [{"variableReplacementStrategy": "originalfirst", "prompt": "<p>In this question we are using the change of base rule:</p>\n<p>\\[\\log_b(a)=\\frac{\\log_c(a)}{\\log_c(b)}\\]</p>\n<p>Notice, $c$ can be any base. Also, notice the big $a$ goes at the top of the fraction, and the little $b$ goes down the bottom.</p>", "variableReplacements": [], "marks": 0, "showCorrectAnswer": true, "scripts": {}, "type": "information"}], "maxMarks": 0, "scripts": {}, "displayType": "radiogroup", "choices": ["<p>$\\log_{\\var{den}}(\\var{num})$</p>", "<p>$\\log_{\\var{num}}(\\var{den})$</p>", "<p>$\\log_{\\var{base2}}(\\var{num-den})$</p>", "<p>$\\log_{\\var{base2}}\\left(\\frac{\\var{num}}{\\var{den}}\\right)$</p>", "<p>$\\log_{\\var{den}}(\\var{base2})$</p>"], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "displayColumns": 0, "matrix": ["1", 0, 0, 0, 0], "minMarks": 0, "shuffleChoices": true, "type": "1_n_2"}], "question_groups": [{"name": "", "pickQuestions": 0, "pickingStrategy": "all-ordered", "questions": []}], "rulesets": {}, "variable_groups": [], "showQuestionGroupNames": false, "name": "David's copy of Logs: change of base", "variables": {"arg1": {"templateType": "anything", "description": "", "name": "arg1", "definition": "random(2..99)", "group": "Ungrouped variables"}, "den": {"templateType": "anything", "description": "", "name": "den", "definition": "random([2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47] except num)", "group": "Ungrouped variables"}, "base2": {"templateType": "anything", "description": "", "name": "base2", "definition": "random(2..10 except base1)", "group": "Ungrouped variables"}, "num": {"templateType": "anything", "description": "", "name": "num", "definition": "random(2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47)", "group": "Ungrouped variables"}, "base1": {"templateType": "anything", "description": "", "name": "base1", "definition": "random(2..10)", "group": "Ungrouped variables"}}, "functions": {}, "statement": "", "variablesTest": {"maxRuns": 100, "condition": ""}, "type": "question", "preamble": {"js": "", "css": ""}, "advice": "", "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/"}]}]}], "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/"}]}