// Numbas version: exam_results_page_options
{"name": "Maria's copy of Rearranging Logarithms involving Indices", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"ungrouped_variables": ["x1", "y1", "z1", "b1", "c", "b4", "b", "b2"], "metadata": {"description": "<p>Use the rule $\\log_a(n^b) = b\\log_a(n)$ to rearrange some expressions.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "variablesTest": {"condition": "", "maxRuns": 100}, "parts": [{"showCorrectAnswer": true, "unitTests": [], "customMarkingAlgorithm": "", "useCustomName": false, "scripts": {}, "gaps": [{"checkingAccuracy": 0.001, "failureRate": 1, "answer": "{x1[3]}^{z1[0]}", "showCorrectAnswer": true, "unitTests": [], "customMarkingAlgorithm": "", "vsetRangePoints": 5, "useCustomName": false, "scripts": {}, "checkingType": "absdiff", "variableReplacements": [], "valuegenerators": [], "customName": "", "vsetRange": [0, 1], "marks": "0.5", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "showPreview": true, "checkVariableNames": false, "type": "jme"}], "variableReplacements": [], "customName": "", "marks": 0, "showFeedbackIcon": true, "prompt": "<p>Simplify the following expressions.</p>\n<p>$\\var{z1[0]}\\log_a(\\var{x1[3]})=\\log_a($ [[0]]$)$</p>", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "sortAnswers": false, "type": "gapfill"}, {"showCorrectAnswer": true, "unitTests": [], "customMarkingAlgorithm": "", "useCustomName": false, "scripts": {}, "gaps": [{"checkingAccuracy": 0.001, "failureRate": 1, "answer": "{z1[5]}", "showCorrectAnswer": true, "unitTests": [], "customMarkingAlgorithm": "", "vsetRangePoints": 5, "useCustomName": false, "scripts": {}, "checkingType": "absdiff", "variableReplacements": [], "valuegenerators": [], "customName": "", "vsetRange": [0, 1], "marks": "0.5", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "showPreview": true, "checkVariableNames": false, "type": "jme"}], "variableReplacements": [], "customName": "", "marks": 0, "showFeedbackIcon": true, "prompt": "<p>Simplify the following expressions. </p>\n<p>$\\log_a(\\var{x1[3]^z1[5]})=$ [[0]] $\\log_a(\\var{x1[3]})$</p>\n<p></p>", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "sortAnswers": false, "type": "gapfill"}], "extensions": [], "rulesets": {}, "variables": {"b4": {"definition": "random(2..4 except b1)", "templateType": "anything", "description": "", "name": "b4", "group": "Ungrouped variables"}, "p": {"definition": "random(3..4)", "templateType": "anything", "description": "", "name": "p", "group": "part c"}, "m": {"definition": "random(2..20)", "templateType": "anything", "description": "", "name": "m", "group": "part c"}, "b2": {"definition": "b-2", "templateType": "anything", "description": "", "name": "b2", "group": "Ungrouped variables"}, "q": {"definition": "v^p", "templateType": "anything", "description": "", "name": "q", "group": "part c"}, "c": {"definition": "b1^b4", "templateType": "anything", "description": "", "name": "c", "group": "Ungrouped variables"}, "b": {"definition": "c/2", "templateType": "anything", "description": "", "name": "b", "group": "Ungrouped variables"}, "z1": {"definition": "repeat(random(2..3),10)", "templateType": "anything", "description": "", "name": "z1", "group": "Ungrouped variables"}, "v": {"definition": "random(2..5)", "templateType": "anything", "description": "", "name": "v", "group": "part c"}, "x1": {"definition": "repeat(random(2..3),8)", "templateType": "anything", "description": "", "name": "x1", "group": "Ungrouped variables"}, "y1": {"definition": "random(2..6)", "templateType": "anything", "description": "", "name": "y1", "group": "Ungrouped variables"}, "b1": {"definition": "random(2..8 #2)", "templateType": "anything", "description": "", "name": "b1", "group": "Ungrouped variables"}}, "name": "Maria's copy of Rearranging Logarithms involving Indices", "advice": "", "variable_groups": [{"variables": ["p", "v", "q", "m"], "name": "part c"}], "statement": "<p>When logarithms involve indices we can rearrange them using the rule,</p>\n<p>\\[\\log_a(x^y)=y\\log_a(x)\\text{.}\\]</p>\n<p>This can also be useful for removing integers from the front of logarithms.</p>", "preamble": {"css": "", "js": ""}, "tags": [], "functions": {}, "type": "question", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Hannah Aldous", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1594/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Hannah Aldous", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1594/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}