// Numbas version: exam_results_page_options
{"name": "David's copy of Logs: scalar multiple to power inside", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": ""}, "extensions": [], "variables": {"ans4": {"templateType": "anything", "definition": "sqrt(square)", "description": "", "name": "ans4", "group": "Ungrouped variables"}, "c": {"templateType": "anything", "definition": "random(-12..12 except [0,1])", "description": "", "name": "c", "group": "Ungrouped variables"}, "d": {"templateType": "anything", "definition": "random(-12..12 except [0,c])", "description": "", "name": "d", "group": "Ungrouped variables"}, "square": {"templateType": "anything", "definition": "random(map(n^2,n,2..12))", "description": "", "name": "square", "group": "Ungrouped variables"}, "root": {"templateType": "anything", "definition": "random(2..5)", "description": "", "name": "root", "group": "Ungrouped variables"}, "mult": {"templateType": "anything", "definition": "random(-12..12 except [-1,0,1,power])", "description": "", "name": "mult", "group": "Ungrouped variables"}, "ans1": {"templateType": "anything", "definition": "c*power", "description": "", "name": "ans1", "group": "Ungrouped variables"}, "power": {"templateType": "anything", "definition": "random(-12..12 except [-1,0,1])", "description": "", "name": "power", "group": "Ungrouped variables"}}, "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"steps": [{"showCorrectAnswer": true, "type": "information", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "prompt": "<p>Here we are using the following log law</p>\n<p>\\[\\log_b(a^n)=n\\log_b(a).\\]</p>\n<p>Notice how exponentiation on the inside of the log became multiplication on the outside.</p>", "marks": 0, "scripts": {}, "variableReplacements": [], "customMarkingAlgorithm": "", "unitTests": [], "showFeedbackIcon": true}], "showCorrectAnswer": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "marks": 0, "scripts": {}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "unitTests": [], "showFeedbackIcon": true, "stepsPenalty": "1", "type": "gapfill", "prompt": "<p>Suppose $\\log_b\\left(a\\right)=\\var{c}$. Evaluate&nbsp;$\\log_b\\left(a^\\var{power}\\right)$ =&nbsp;[[0]].</p>", "gaps": [{"correctAnswerStyle": "plain", "minValue": "{ans1}", "maxValue": "{ans1}", "mustBeReducedPC": 0, "showCorrectAnswer": true, "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "marks": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "unitTests": [], "showFeedbackIcon": true, "allowFractions": false, "type": "numberentry", "mustBeReduced": false}], "sortAnswers": false}, {"steps": [{"showCorrectAnswer": true, "type": "information", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "prompt": "<p>Here we are using the following log law</p>\n<p>\\[\\log_b(a^n)=n\\log_b(a).\\]</p>\n<p>Notice how exponentiation on the inside of the log became multiplication on the outside.</p>", "marks": 0, "scripts": {}, "variableReplacements": [], "customMarkingAlgorithm": "", "unitTests": [], "showFeedbackIcon": true}], "showCorrectAnswer": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "marks": 0, "scripts": {}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "unitTests": [], "showFeedbackIcon": true, "stepsPenalty": "1", "type": "gapfill", "prompt": "<p>$\\var{mult}\\log_b\\left(a\\right)$&nbsp;is equivalent to&nbsp;$\\log_b\\large($[[0]]$\\large)$.</p>", "gaps": [{"vsetRange": ["1", "1.5"], "vsetRangePoints": 5, "showCorrectAnswer": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "marks": 1, "scripts": {}, "checkingType": "absdiff", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "answer": "a^{mult}", "showFeedbackIcon": true, "checkingAccuracy": 0.001, "type": "jme", "checkVariableNames": false, "failureRate": 1, "unitTests": [], "showPreview": false, "expectedVariableNames": []}], "sortAnswers": false}, {"steps": [{"showCorrectAnswer": true, "type": "information", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "prompt": "<p>Here we are using the following log law</p>\n<p>\\[\\log_b(a^n)=n\\log_b(a).\\]</p>\n<p>Notice how exponentiation on the inside of the log became multiplication on the outside.</p>\n<p></p>\n<p>But we are also using that</p>\n<p>\\[x^{1/n}=\\sqrt[n]{x}.\\]</p>", "marks": 0, "scripts": {}, "variableReplacements": [], "customMarkingAlgorithm": "", "unitTests": [], "showFeedbackIcon": true}], "showCorrectAnswer": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "marks": 0, "scripts": {}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "unitTests": [], "showFeedbackIcon": true, "stepsPenalty": "1", "type": "gapfill", "prompt": "<p>Suppose $\\log_b\\left(x\\right)=\\var{d}$. Evaluate&nbsp;$\\log_b\\left(\\sqrt[\\var{root}]{x}\\right)$ =&nbsp;[[0]].</p>", "gaps": [{"correctAnswerStyle": "plain", "minValue": "{d}/{root}", "maxValue": "{d}/{root}", "mustBeReducedPC": 0, "showCorrectAnswer": true, "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "marks": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "unitTests": [], "showFeedbackIcon": true, "allowFractions": true, "type": "numberentry", "mustBeReduced": false}], "sortAnswers": false}, {"steps": [{"showCorrectAnswer": true, "type": "information", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "prompt": "<p>Here we are using the following log law</p>\n<p>\\[\\log_b(a^n)=n\\log_b(a).\\]</p>\n<p>Notice how exponentiation on the inside of the log became multiplication on the outside.</p>\n<p></p>\n<p>But we are also using that</p>\n<p>\\[x^{1/n}=\\sqrt[n]{x}.\\]</p>", "marks": 0, "scripts": {}, "variableReplacements": [], "customMarkingAlgorithm": "", "unitTests": [], "showFeedbackIcon": true}], "showCorrectAnswer": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "marks": 0, "scripts": {}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "unitTests": [], "showFeedbackIcon": true, "stepsPenalty": "1", "type": "gapfill", "prompt": "<p>$\\frac{1}{2}\\log_b\\left(\\var{square}\\right)$&nbsp;is equivalent to&nbsp;$\\log_b\\large($[[0]]$\\large)$.<br/><br/></p>", "gaps": [{"correctAnswerStyle": "plain", "minValue": "{ans4}", "maxValue": "{ans4}", "mustBeReducedPC": 0, "showCorrectAnswer": true, "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "marks": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "unitTests": [], "showFeedbackIcon": true, "allowFractions": false, "type": "numberentry", "mustBeReduced": false}], "sortAnswers": false}], "advice": "<p>Given the equation $ \\log(a^n)$ we can rearrange this as $n\\log(a)$</p>\n<p>As $\\sqrt[n]{x}$ = $n^{\\frac{1}{n}}$,&nbsp;&nbsp;$ \\log(\\sqrt[n]{a}) = \\frac{\\log(a)}{n}$</p>\n<p></p>", "variable_groups": [], "name": "David's copy of Logs: scalar multiple to power inside", "functions": {}, "statement": "<p>Based on the definition of logarithms&nbsp;determine the following:</p>", "tags": [], "rulesets": {}, "preamble": {"js": "", "css": ""}, "ungrouped_variables": ["c", "power", "ans1", "mult", "d", "root", "square", "ans4"], "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/"}]}]}], "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/"}]}