// Numbas version: exam_results_page_options {"name": "Maria's copy of Using the Logarithm Equivalence $\\log_ba=c \\Longleftrightarrow a=b^c$", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"useCustomName": false, "prompt": "

Rearrange the equation to find $x$.

\n

$\\log_\\var{f}(x)=\\var{f1}$ 

\n

$x=$ [[0]]

", "scripts": {}, "sortAnswers": false, "customName": "", "gaps": [{"useCustomName": false, "checkVariableNames": false, "scripts": {}, "failureRate": 1, "checkingType": "absdiff", "valuegenerators": [], "vsetRangePoints": 5, "customName": "", "showPreview": true, "unitTests": [], "marks": 1, "variableReplacementStrategy": "originalfirst", "type": "jme", "showFeedbackIcon": true, "showCorrectAnswer": true, "vsetRange": [0, 1], "variableReplacements": [], "customMarkingAlgorithm": "", "checkingAccuracy": 0.001, "extendBaseMarkingAlgorithm": true, "answer": "{f^f1}"}], "unitTests": [], "marks": 0, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showFeedbackIcon": true, "showCorrectAnswer": true, "variableReplacements": [], "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true}, {"useCustomName": false, "scripts": {}, "maxMarks": 0, "minMarks": 0, "marks": 0, "type": "m_n_2", "showFeedbackIcon": true, "shuffleChoices": true, "customMarkingAlgorithm": "", "warningType": "none", "variableReplacements": [], "distractors": ["", "", "", ""], "showCellAnswerState": true, "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "prompt": "

Which of the following expressions are equivalent to $x$?

", "choices": ["

$\\log_a(a^x)$

", "

$e^{\\ln(x)}$

", "

$\\ln(10^x)$

", "$\\log_a (10^x)$"], "displayType": "checkbox", "customName": "", "unitTests": [], "maxAnswers": 0, "variableReplacementStrategy": "originalfirst", "minAnswers": 0, "displayColumns": 0, "matrix": ["1", "1", "0", "0"]}], "extensions": [], "tags": [], "ungrouped_variables": ["f", "f2", "f1", "f3", "f4", "f5"], "preamble": {"js": "", "css": ""}, "advice": "", "functions": {}, "variable_groups": [{"name": "part 2", "variables": ["g3", "g2", "g4", "g1"]}, {"name": "part3", "variables": ["h1", "h2"]}], "name": "Maria's copy of Using the Logarithm Equivalence $\\log_ba=c \\Longleftrightarrow a=b^c$", "variables": {"g2": {"description": "", "name": "g2", "templateType": "anything", "definition": "random(2..10except g1)", "group": "part 2"}, "f1": {"description": "", "name": "f1", "templateType": "anything", "definition": "random(2..4 except f)", "group": "Ungrouped variables"}, "f5": {"description": "", "name": "f5", "templateType": "anything", "definition": "random(2..6 except f1)", "group": "Ungrouped variables"}, "g3": {"description": "", "name": "g3", "templateType": "anything", "definition": "random(2..10except g1 g2)", "group": "part 2"}, "h1": {"description": "", "name": "h1", "templateType": "anything", "definition": "random(1..10 except h2)", "group": "part3"}, "g1": {"description": "", "name": "g1", "templateType": "anything", "definition": "random(2..10)", "group": "part 2"}, "f": {"description": "", "name": "f", "templateType": "anything", "definition": "random(2..4)", "group": "Ungrouped variables"}, "f2": {"description": "", "name": "f2", "templateType": "anything", "definition": "random(2..10 except f3 f)", "group": "Ungrouped variables"}, "h2": {"description": "", "name": "h2", "templateType": "anything", "definition": "random(2..4)", "group": "part3"}, "f3": {"description": "", "name": "f3", "templateType": "anything", "definition": "random(3..8)", "group": "Ungrouped variables"}, "f4": {"description": "", "name": "f4", "templateType": "anything", "definition": "random(5..12 except f2 f)", "group": "Ungrouped variables"}, "g4": {"description": "", "name": "g4", "templateType": "anything", "definition": "random(2..10except g1 g2 g3)", "group": "part 2"}}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "

Rearrange some expressions involving logarithms by applying the relation $\\log_b(a) = c \\iff a = b^c$.

"}, "statement": "

Changing the subject of an equation involving logarithms often requires the use of the equivalence

\n

\\[\\log_ba=c \\Longleftrightarrow a=b^c\\text{.}\\]

", "rulesets": {}, "variablesTest": {"maxRuns": 100, "condition": ""}, "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/"}]}