// 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": [{"name": "Solve a logarithmic equation", "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>", "variable_groups": [], "ungrouped_variables": ["a", "b", "c", "d"], "functions": {}, "extensions": [], "variablesTest": {"condition": "", "maxRuns": 100}, "type": "question", "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>", "preamble": {"js": "", "css": ""}, "tags": [], "parts": [{"showFeedbackIcon": true, "variableReplacements": [], "marks": 0, "scripts": {}, "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>", "gaps": [{"precisionMessage": "You have not given your answer to the correct precision.", "variableReplacements": [], "correctAnswerStyle": "plain", "scripts": {}, "strictPrecision": false, "maxValue": "((10^(d/a))-c)/b", "showPrecisionHint": false, "precision": "3", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "marks": "2", "precisionType": "dp", "allowFractions": false, "minValue": "((10^(d/a))-c)/b", "precisionPartialCredit": 0, "correctAnswerFraction": false, "mustBeReducedPC": 0, "mustBeReduced": false}], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "gapfill"}], "rulesets": {}, "metadata": {"description": "<p>Solve a logarithmic equation</p>", "licence": "Creative Commons Attribution 4.0 International"}, "variables": {"b": {"templateType": "randrange", "description": "", "definition": "random(2..6#1)", "group": "Ungrouped variables", "name": "b"}, "a": {"templateType": "randrange", "description": "", "definition": "random(2..8#1)", "group": "Ungrouped variables", "name": "a"}, "d": {"templateType": "randrange", "description": "", "definition": "random(1..6#1)", "group": "Ungrouped variables", "name": "d"}, "c": {"templateType": "randrange", "description": "", "definition": "random(2..10#1)", "group": "Ungrouped variables", "name": "c"}}, "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}