// Numbas version: exam_results_page_options
{"name": "Logarithms [L6]", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"extensions": [], "advice": "<h4></h4>\n<h4></h4>", "name": "Logarithms [L6]", "tags": ["L6"], "rulesets": {}, "variable_groups": [{"variables": ["g3", "g2", "g4", "g1"], "name": "part 2"}, {"variables": ["h1", "h2"], "name": "part3"}], "variables": {"g1": {"description": "", "templateType": "anything", "name": "g1", "definition": "random(2..10)", "group": "part 2"}, "f5": {"description": "", "templateType": "anything", "name": "f5", "definition": "random(2..6 except f1)", "group": "Ungrouped variables"}, "f4": {"description": "", "templateType": "anything", "name": "f4", "definition": "random(5..12 except f2 f)", "group": "Ungrouped variables"}, "f": {"description": "", "templateType": "anything", "name": "f", "definition": "random(2..10)", "group": "Ungrouped variables"}, "g4": {"description": "", "templateType": "anything", "name": "g4", "definition": "random(2..10except g1 g2 g3)", "group": "part 2"}, "g2": {"description": "", "templateType": "anything", "name": "g2", "definition": "random(2..10except g1)", "group": "part 2"}, "g3": {"description": "", "templateType": "anything", "name": "g3", "definition": "random(2..10except g1 g2)", "group": "part 2"}, "h2": {"description": "", "templateType": "anything", "name": "h2", "definition": "random(2..4)", "group": "part3"}, "f1": {"description": "", "templateType": "anything", "name": "f1", "definition": "random(2..5 except f)", "group": "Ungrouped variables"}, "f2": {"description": "", "templateType": "anything", "name": "f2", "definition": "random(2..10 except f3 f)", "group": "Ungrouped variables"}, "f3": {"description": "", "templateType": "anything", "name": "f3", "definition": "random(3..8)", "group": "Ungrouped variables"}, "h1": {"description": "", "templateType": "anything", "name": "h1", "definition": "random(1..10 except h2)", "group": "part3"}}, "ungrouped_variables": ["f", "f2", "f1", "f3", "f4", "f5"], "preamble": {"css": "", "js": ""}, "parts": [{"variableReplacements": [], "gaps": [{"variableReplacements": [], "showPreview": true, "answer": "{f^f1}", "expectedVariableNames": [], "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "vsetRange": [0, 1], "checkVariableNames": false, "vsetRangePoints": 5, "marks": 1, "type": "jme", "checkingType": "absdiff", "unitTests": [], "checkingAccuracy": 0.001, "showCorrectAnswer": true, "scripts": {}, "customMarkingAlgorithm": "", "failureRate": 1}], "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "sortAnswers": false, "type": "gapfill", "marks": 0, "prompt": "<p>Calculate&nbsp;$x$.</p>\n<p>$\\log_\\var{f}(x)=\\var{f1}$&nbsp;</p>\n<p>$x=$&nbsp;[[0]]</p>", "unitTests": [], "showCorrectAnswer": true, "scripts": {}, "customMarkingAlgorithm": ""}, {"extendBaseMarkingAlgorithm": true, "distractors": ["", "", "", "", "", ""], "choices": ["<p>$\\log_a(a^x)$</p>", "<p>$a^{\\log_a(x)}$</p>", "<p>$e^{\\ln(x)}$</p>", "<p>$\\log_{10}(x)$</p>", "<p>$\\log_e(x)$</p>", "<p>$\\ln(e^x)$</p>"], "minMarks": 0, "type": "m_n_2", "minAnswers": 0, "warningType": "none", "customMarkingAlgorithm": "", "displayColumns": 0, "variableReplacements": [], "maxMarks": 0, "marks": 0, "displayType": "checkbox", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "shuffleChoices": true, "matrix": ["0.5", "0.5", "0.5", "-0.5", "-0.5", "0.5"], "prompt": "<pre class=\"tw-data-text tw-ta tw-text-small\" data-placeholder=\"Translation\" id=\"tw-target-text\" data-fulltext=\"\" dir=\"ltr\">Which of these is equivalent to x? <br/>(There may be more than one correct answer)</pre>", "unitTests": [], "showCorrectAnswer": true, "scripts": {}, "maxAnswers": 0}], "statement": "<p>We define the logarithm of a positive number $a$ in this way:</p>\n<p></p>\n<p>\\[\\log_ba=c \\Longleftrightarrow a=b^c \\space \\text{where $b&gt;0$ is the base number.}\\]</p>", "functions": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "metadata": {"description": "<p>Rearrange some expressions involving logarithms by applying the relation&nbsp;$\\log_b(a) = c \\iff a = b^c$.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "contributors": [{"name": "Ida Landg\u00e4rds", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2336/"}, {"name": "Abbi Mullins", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2466/"}]}]}], "contributors": [{"name": "Ida Landg\u00e4rds", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2336/"}, {"name": "Abbi Mullins", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2466/"}]}