// Numbas version: exam_results_page_options
{"name": "Solve a logarithmic equation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"statement": "<p>Calculate the value of \\(x\\) that satisfies the following equation:</p>\n<p style=\"padding-left: 30px;\">\\(\\var{a}log(\\var{b}x+\\var{c})=\\var{d}\\)</p>", "variable_groups": [], "extensions": [], "tags": [], "parts": [{"gaps": [{"precisionMessage": "You have not given your answer to the correct precision.", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "marks": "2", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "precisionType": "dp", "allowFractions": false, "strictPrecision": false, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "correctAnswerFraction": false, "scripts": {}, "maxValue": "((10^(d/a))-c)/b", "variableReplacements": [], "showCorrectAnswer": true, "minValue": "((10^(d/a))-c)/b", "precision": "3", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill", "showFeedbackIcon": true, "prompt": "<p>Input your answer correct to three decimal places.</p>\n<p>\\(x = \\)&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst"}], "variables": {"d": {"templateType": "randrange", "group": "Ungrouped variables", "definition": "random(1..6#1)", "name": "d", "description": ""}, "b": {"templateType": "randrange", "group": "Ungrouped variables", "definition": "random(2..6#1)", "name": "b", "description": ""}, "a": {"templateType": "randrange", "group": "Ungrouped variables", "definition": "random(2..8#1)", "name": "a", "description": ""}, "c": {"templateType": "randrange", "group": "Ungrouped variables", "definition": "random(2..10#1)", "name": "c", "description": ""}}, "name": "Solve a logarithmic equation", "preamble": {"css": "", "js": ""}, "rulesets": {}, "functions": {}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Solve a logarithmic equation</p>"}, "advice": "<p style=\"text-align: left; padding-left: 30px;\">\\(\\var{a}log(\\var{b}x+\\var{c})=\\var{d}\\)</p>\n<p>Divide across by \\(\\var{a}\\)</p>\n<p style=\"padding-left: 30px;\">\\(log(\\var{b}x+\\var{c})=\\var{d}/\\var{a}=\\simplify{{d}/{a}}\\)</p>\n<p style=\"padding-left: 30px;\">\\(\\var{b}x+\\var{c}=10^{\\simplify{{d}/{a}}}\\)</p>\n<p style=\"padding-left: 30px;\">\\(\\var{b}x+\\var{c}=\\simplify{10^{{d}/{a}}}\\)</p>\n<p style=\"padding-left: 30px;\">\\(\\var{b}x=\\simplify{10^{{d}/{a}}}-\\var{c}\\)</p>\n<p style=\"padding-left: 30px;\">\\(\\var{b}x=\\simplify{10^{{d}/{a}}-{c}}\\)</p>\n<p style=\"padding-left: 30px;\">\\(x=\\simplify{(10^{{d}/{a}}-{c})/{b}}\\)</p>", "variablesTest": {"maxRuns": 100, "condition": ""}, "ungrouped_variables": ["a", "b", "c", "d"], "type": "question", "contributors": [{"name": "Nigel Atkins", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/275/"}]}]}], "contributors": [{"name": "Nigel Atkins", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/275/"}]}