// Numbas version: finer_feedback_settings
{"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": [{"name": "Solving Logarithms for Geosciences", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": ""}, "statement": "<p>Solve these equations for x, give your answer as integer or fraction.</p>", "functions": {}, "ungrouped_variables": ["a1", "a2", "a3", "a4", "b1", "b2", "b3", "b4", "c1", "c2", "c3", "c4", "c5", "a", "b", "d1", "d2", "d3", "d4"], "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "variables": {"d2": {"templateType": "anything", "name": "d2", "description": "", "group": "Ungrouped variables", "definition": "random(2..5)"}, "d4": {"templateType": "anything", "name": "d4", "description": "", "group": "Ungrouped variables", "definition": "+a+b"}, "b2": {"templateType": "anything", "name": "b2", "description": "", "group": "Ungrouped variables", "definition": "random(2..9)"}, "d1": {"templateType": "anything", "name": "d1", "description": "", "group": "Ungrouped variables", "definition": "random(2..6)"}, "c2": {"templateType": "anything", "name": "c2", "description": "", "group": "Ungrouped variables", "definition": "random(2..19)"}, "d3": {"templateType": "anything", "name": "d3", "description": "", "group": "Ungrouped variables", "definition": "a*b"}, "c5": {"templateType": "anything", "name": "c5", "description": "", "group": "Ungrouped variables", "definition": "random(1..5)"}, "c1": {"templateType": "anything", "name": "c1", "description": "", "group": "Ungrouped variables", "definition": "random(2..5)"}, "b": {"templateType": "anything", "name": "b", "description": "", "group": "Ungrouped variables", "definition": "floor(3a/2)"}, "b4": {"templateType": "anything", "name": "b4", "description": "", "group": "Ungrouped variables", "definition": "random(1..19)"}, "c3": {"templateType": "anything", "name": "c3", "description": "", "group": "Ungrouped variables", "definition": "random(2..9 except c2)"}, "a2": {"templateType": "anything", "name": "a2", "description": "", "group": "Ungrouped variables", "definition": "random([4,6,8,10])"}, "a4": {"templateType": "anything", "name": "a4", "description": "", "group": "Ungrouped variables", "definition": "random(2..3 except a2 except a3)"}, "c4": {"templateType": "anything", "name": "c4", "description": "", "group": "Ungrouped variables", "definition": "random(2..9 except c3)"}, "a3": {"templateType": "anything", "name": "a3", "description": "", "group": "Ungrouped variables", "definition": "a2/2"}, "b3": {"templateType": "anything", "name": "b3", "description": "", "group": "Ungrouped variables", "definition": "random(2..5)"}, "b1": {"templateType": "anything", "name": "b1", "description": "", "group": "Ungrouped variables", "definition": "random(2..6)"}, "a1": {"templateType": "anything", "name": "a1", "description": "", "group": "Ungrouped variables", "definition": "2a2^((a4)-1)"}, "a": {"templateType": "anything", "name": "a", "description": "", "group": "Ungrouped variables", "definition": "random(1..9)"}}, "preamble": {"js": "", "css": ""}, "tags": [], "variable_groups": [], "type": "question", "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>", "extensions": [], "parts": [{"gaps": [{"correctAnswerFraction": false, "maxValue": "{a1}", "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": 1, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "scripts": {}, "variableReplacements": [], "type": "numberentry", "allowFractions": false, "minValue": "{a1}"}], "variableReplacementStrategy": "originalfirst", "scripts": {}, "showFeedbackIcon": true, "showCorrectAnswer": true, "stepsPenalty": 0, "marks": 0, "type": "gapfill", "variableReplacements": [], "prompt": "<p>$\\log_\\var{a2}\\var{a3}+\\log_\\var{a2}x = \\var{a4}$</p>\n<p>$x=$[[0]]</p>", "steps": [{"variableReplacementStrategy": "originalfirst", "scripts": {}, "showFeedbackIcon": true, "showCorrectAnswer": true, "type": "extension", "marks": 1, "variableReplacements": [], "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>"}]}, {"gaps": [{"correctAnswerFraction": false, "maxValue": "{b2}*({b1}^{b3})-{b4}", "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": 1, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "scripts": {}, "variableReplacements": [], "type": "numberentry", "allowFractions": false, "minValue": "{b2}*({b1}^{b3})-{b4}"}], "variableReplacementStrategy": "originalfirst", "scripts": {}, "showFeedbackIcon": true, "showCorrectAnswer": true, "stepsPenalty": 0, "marks": 0, "type": "gapfill", "variableReplacements": [], "prompt": "<p>$\\log_\\var{b1}(x+\\var{b4})-\\log_\\var{b1}\\var{b2} = \\var{b3}$</p>\n<p>$x=$[[0]]</p>", "steps": [{"variableReplacementStrategy": "originalfirst", "scripts": {}, "showFeedbackIcon": true, "showCorrectAnswer": true, "type": "extension", "marks": 1, "variableReplacements": [], "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>"}]}, {"gaps": [{"correctAnswerFraction": true, "maxValue": "({c4}*({c1}^{c5}))/(({c3}*({c1}^{c5}))-{c2})", "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": 1, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "scripts": {}, "variableReplacements": [], "type": "numberentry", "allowFractions": true, "minValue": "({c4}*({c1}^{c5}))/(({c3}*({c1}^{c5}))-{c2})"}], "variableReplacementStrategy": "originalfirst", "scripts": {}, "showFeedbackIcon": true, "showCorrectAnswer": true, "type": "gapfill", "marks": 0, "variableReplacements": [], "prompt": "<p>$\\log_\\var{c1}\\var{c2}x-\\log_\\var{c1}(\\var{c3}x-\\var{c4}) = \\var{c5}$</p>\n<p>$x=$[[0]]</p>"}], "contributors": [{"name": "Jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/353/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/353/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}