// Numbas version: finer_feedback_settings
{"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": [{"extensions": [], "parts": [{"scripts": {}, "marks": 0, "variableReplacements": [], "type": "gapfill", "showCorrectAnswer": true, "prompt": "<p>Calculate the value of \\(x\\) that satisfies the equation when&nbsp; \\(y=\\var{d}\\).</p>\n<p>Input your answer correct to three decimal places.</p>\n<p>\\(x = \\)&nbsp;[[0]]</p>", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "correctAnswerStyle": "plain", "scripts": {}, "maxValue": "((10^(d/a))-c)/b", "mustBeReduced": false, "showCorrectAnswer": true, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "correctAnswerFraction": false, "allowFractions": false, "variableReplacements": [], "strictPrecision": false, "marks": "2", "minValue": "((10^(d/a))-c)/b", "precisionType": "dp", "showPrecisionHint": false, "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "precision": "3"}]}], "statement": "<p>Given the following logarithmic equation:</p>\n<p style=\"padding-left: 30px;\">\\(y=\\var{a}log(\\var{b}x+\\var{c}))\\)</p>\n<p></p>", "rulesets": {}, "variable_groups": [], "ungrouped_variables": ["a", "b", "c", "d"], "name": "Solve a logarithmic equation", "functions": {}, "tags": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Solve a logarithmic equation</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "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>", "preamble": {"css": "", "js": ""}, "variables": {"b": {"name": "b", "templateType": "randrange", "group": "Ungrouped variables", "description": "", "definition": "random(2..6#1)"}, "c": {"name": "c", "templateType": "randrange", "group": "Ungrouped variables", "description": "", "definition": "random(2..10#1)"}, "a": {"name": "a", "templateType": "randrange", "group": "Ungrouped variables", "description": "", "definition": "random(2..8#1)"}, "d": {"name": "d", "templateType": "randrange", "group": "Ungrouped variables", "description": "", "definition": "random(1..6#1)"}}, "type": "question", "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}]}