// Numbas version: exam_results_page_options
{"name": "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": [{"variables": {"ans4": {"templateType": "anything", "name": "ans4", "description": "", "definition": "sqrt(square)", "group": "Ungrouped variables"}, "mult": {"templateType": "anything", "name": "mult", "description": "", "definition": "random(-12..12 except [-1,0,1,power])", "group": "Ungrouped variables"}, "c": {"templateType": "anything", "name": "c", "description": "", "definition": "random(-12..12 except [0,1])", "group": "Ungrouped variables"}, "d": {"templateType": "anything", "name": "d", "description": "", "definition": "random(-12..12 except [0,c])", "group": "Ungrouped variables"}, "ans1": {"templateType": "anything", "name": "ans1", "description": "", "definition": "c*power", "group": "Ungrouped variables"}, "power": {"templateType": "anything", "name": "power", "description": "", "definition": "random(-12..12 except [-1,0,1])", "group": "Ungrouped variables"}, "root": {"templateType": "anything", "name": "root", "description": "", "definition": "random(2..5)", "group": "Ungrouped variables"}, "square": {"templateType": "anything", "name": "square", "description": "", "definition": "random(map(n^2,n,2..12))", "group": "Ungrouped variables"}}, "statement": "<p>Based on the definition of logarithms&nbsp;determine the following:</p>", "name": "Logs: scalar multiple to power inside", "parts": [{"marks": 0, "customMarkingAlgorithm": "", "steps": [{"marks": 0, "customMarkingAlgorithm": "", "scripts": {}, "extendBaseMarkingAlgorithm": true, "customName": "", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "information", "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>", "unitTests": [], "useCustomName": false, "variableReplacements": []}], "scripts": {}, "extendBaseMarkingAlgorithm": true, "customName": "", "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "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", "marks": 1, "mustBeReduced": false, "customMarkingAlgorithm": "", "scripts": {}, "extendBaseMarkingAlgorithm": true, "customName": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "minValue": "{ans1}", "mustBeReducedPC": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "numberentry", "maxValue": "{ans1}", "allowFractions": false, "unitTests": [], "useCustomName": false, "correctAnswerFraction": false, "variableReplacements": []}], "unitTests": [], "useCustomName": false, "stepsPenalty": "1", "variableReplacements": []}, {"marks": 0, "customMarkingAlgorithm": "", "steps": [{"marks": 0, "customMarkingAlgorithm": "", "scripts": {}, "extendBaseMarkingAlgorithm": true, "customName": "", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "information", "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>", "unitTests": [], "useCustomName": false, "variableReplacements": []}], "scripts": {}, "extendBaseMarkingAlgorithm": true, "customName": "", "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "gapfill", "prompt": "<p>$\\var{mult}\\log_b\\left(a\\right)$&nbsp;is equivalent to&nbsp;$\\log_b\\large($[[0]]$\\large)$.</p>", "gaps": [{"marks": 1, "vsetRangePoints": 5, "customMarkingAlgorithm": "", "checkingAccuracy": 0.001, "scripts": {}, "extendBaseMarkingAlgorithm": true, "customName": "", "showPreview": false, "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "answer": "a^{mult}", "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "jme", "failureRate": 1, "valuegenerators": [{"name": "a", "value": ""}], "vsetRange": ["1", "1.5"], "unitTests": [], "useCustomName": false, "checkVariableNames": false, "variableReplacements": []}], "unitTests": [], "useCustomName": false, "stepsPenalty": "1", "variableReplacements": []}, {"marks": 0, "customMarkingAlgorithm": "", "steps": [{"marks": 0, "customMarkingAlgorithm": "", "scripts": {}, "extendBaseMarkingAlgorithm": true, "customName": "", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "information", "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>", "unitTests": [], "useCustomName": false, "variableReplacements": []}], "scripts": {}, "extendBaseMarkingAlgorithm": true, "customName": "", "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "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", "marks": 1, "mustBeReduced": false, "customMarkingAlgorithm": "", "scripts": {}, "extendBaseMarkingAlgorithm": true, "customName": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "minValue": "{d}/{root}", "mustBeReducedPC": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "numberentry", "maxValue": "{d}/{root}", "allowFractions": true, "unitTests": [], "useCustomName": false, "correctAnswerFraction": true, "variableReplacements": []}], "unitTests": [], "useCustomName": false, "stepsPenalty": "1", "variableReplacements": []}, {"marks": 0, "customMarkingAlgorithm": "", "steps": [{"marks": 0, "customMarkingAlgorithm": "", "scripts": {}, "extendBaseMarkingAlgorithm": true, "customName": "", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "information", "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>", "unitTests": [], "useCustomName": false, "variableReplacements": []}], "scripts": {}, "extendBaseMarkingAlgorithm": true, "customName": "", "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "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", "marks": 1, "mustBeReduced": false, "customMarkingAlgorithm": "", "scripts": {}, "extendBaseMarkingAlgorithm": true, "customName": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "minValue": "{ans4}", "mustBeReducedPC": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "numberentry", "maxValue": "{ans4}", "allowFractions": false, "unitTests": [], "useCustomName": false, "correctAnswerFraction": false, "variableReplacements": []}], "unitTests": [], "useCustomName": false, "stepsPenalty": "1", "variableReplacements": []}], "functions": {}, "rulesets": {}, "variable_groups": [], "preamble": {"css": "", "js": ""}, "tags": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "extensions": [], "ungrouped_variables": ["c", "power", "ans1", "mult", "d", "root", "square", "ans4"], "advice": "", "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": ""}, "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/"}]}