// Numbas version: exam_results_page_options
{"name": "Solving Logarithms for Geosciences", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"showFeedbackIcon": true, "showCorrectAnswer": true, "gaps": [{"showCorrectAnswer": true, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "type": "numberentry", "scripts": {}, "variableReplacements": [], "allowFractions": false, "minValue": "{a1}", "maxValue": "{a1}", "marks": 1, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false}], "prompt": "<p>$\\log_\\var{a2}\\var{a3}+\\log_\\var{a2}x = \\var{a4}$</p>\n<p>$x=$[[0]]</p>", "marks": 0, "stepsPenalty": 0, "scripts": {}, "variableReplacementStrategy": "originalfirst", "steps": [{"showFeedbackIcon": true, "showCorrectAnswer": true, "prompt": "<p>First you need to use the law of logarithm to combine the two logs on the left handside &nbsp;to one:</p>\n<p>$\\log_\\var{a2}(\\var{a3}\\times\\var{a2}x) = \\var{a4}$</p>\n<p>Then use the definition of log to change it to exponient form.</p>\n<p></p>", "marks": 1, "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "extension", "variableReplacements": []}], "type": "gapfill", "variableReplacements": []}, {"showFeedbackIcon": true, "showCorrectAnswer": true, "gaps": [{"showCorrectAnswer": true, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "type": "numberentry", "scripts": {}, "variableReplacements": [], "allowFractions": false, "minValue": "{b2}*({b1}^{b3})-{b4}", "maxValue": "{b2}*({b1}^{b3})-{b4}", "marks": 1, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false}], "prompt": "<p>$\\log_\\var{b1}(x+\\var{b4})-\\log_\\var{b1}\\var{b2} = \\var{b3}$</p>\n<p>$x=$[[0]]</p>", "marks": 0, "stepsPenalty": 0, "scripts": {}, "variableReplacementStrategy": "originalfirst", "steps": [{"showFeedbackIcon": true, "showCorrectAnswer": true, "prompt": "<p>Similar to the first question, you need to use the law of logarithm to combine the two logs on the left handside&nbsp;to one:</p>\n<p>Then use the definition of log to change it to exponient form.</p>\n<p></p>", "marks": 1, "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "extension", "variableReplacements": []}], "type": "gapfill", "variableReplacements": []}, {"showFeedbackIcon": true, "showCorrectAnswer": true, "prompt": "<p>$\\log_\\var{c1}\\var{c2}x-\\log_\\var{c1}(\\var{c3}x-\\var{c4}) = \\var{c5}$</p>\n<p>$x=$[[0]]</p>", "marks": 0, "gaps": [{"showCorrectAnswer": true, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "type": "numberentry", "scripts": {}, "variableReplacements": [], "allowFractions": true, "minValue": "({c4}*({c1}^{c5}))/(({c3}*({c1}^{c5}))-{c2})", "maxValue": 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"d3", "d4"], "preamble": {"js": "", "css": ""}, "advice": "<p>We want to solve for x. After simplifying, in each case we end up with $\\log_a{f(x)} = b$, so we raise both sides as a power of $a$ to get $a^{\\log_a{f(x)}} = a^b$ which simplifies (by laws of logarithms) to $f(x)=a^b$. We then solve for x accordingly.</p>\n<p>Use of the laws of logarithms is crucial here:</p>\n<p>$\\log{a} + \\log{b} = \\log{ab}$</p>\n<p>$\\log{a} - \\log{b} = \\log{\\frac{a}{b}}$</p>\n<p>$\\log{a^n} = n\\log{a}$</p>", "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "variable_groups": [], "extensions": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "rulesets": {}, "functions": {}, "statement": "<p>Solve these equations for x, give your answer as integer or fraction.</p>", "type": "question", "contributors": [{"name": "Jean jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/353/"}]}]}], "contributors": [{"name": "Jean jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/353/"}]}