// Numbas version: finer_feedback_settings
{"name": "Solving equations that contain natural log", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["n1", "n2", "n3", "ans1", "n4", "n5", "n6", "n7", "ans2", "n8", "n9", "n10", "ans3"], "name": "Solving equations that contain natural log", "tags": ["rebel", "rebelmaths"], "preamble": {"css": "", "js": ""}, "advice": "<p>i) $\\var{n1}\\ln(\\var{n2}x) = \\var{n3}$</p>\n<p>$\\ln(\\var{n2}x) = \\frac{\\var{n3}}{\\var{n1}}$</p>\n<p>Next,</p>\n<p>$\\var{n2}x = e^{\\frac{\\var{n3}}{\\var{n1}}}$</p>\n<p>$x= \\frac{e^{(\\frac{\\var{n3}}{\\var{n1}})} }{\\var{n2}} = \\var{ans1}$</p>\n<p></p>\n<p>ii) $\\var{n4}\\ln(\\frac{\\var{n5}x}{\\var{n6}}) = \\var{n7}$</p>\n<p>$\\ln(\\frac{\\var{n5}x}{\\var{n6}}) =\\frac{ \\var{n7}}{\\var{n4}}$</p>\n<p>Next,</p>\n<p>$\\frac{\\var{n5}x}{\\var{n6}}=e^{\\frac{ \\var{n7}}{\\var{n4}}}$</p>\n<p>$x= e^{(\\frac{\\var{n7}}{\\var{n4}})} \\times \\frac{\\var{n6}}{\\var{n5}}&nbsp;= \\var{ans2}$</p>\n<p></p>\n<p></p>\n<p>iii) $\\var{n8} = \\ln(\\frac{\\var{n9}}{\\var{n10}x})$</p>\n<p>$e^{\\var{n8}}=\\frac{\\var{n9}}{\\var{n10}x}$</p>\n<p>$\\var{n10}xe^{\\var{n8}}=\\var{n9}$</p>\n<p>$x= \\frac{\\var{n9}}{(\\var{n10}&nbsp;\\times e^\\var{n8})} = \\var{ans3}$</p>", "rulesets": {}, "parts": [{"prompt": "<p>i) $\\var{n1}\\ln(\\var{n2}x) = \\var{n3}$</p>\n<p>$x = $[[0]]</p>\n<p>ii) $\\var{n4}\\ln(\\frac{\\var{n5}x}{\\var{n6}}) = \\var{n7}$</p>\n<p>$x = $[[1]]</p>\n<p>iii) $\\var{n8} = \\ln(\\frac{\\var{n9}}{\\var{n10}x})$</p>\n<p><em>Give correct to 4 decimal places:</em></p>\n<p>$x = $[[2]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{ans1}", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "minValue": "{ans1}", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{ans2}", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "minValue": "{ans2}", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "4", "maxValue": "{ans3}", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "minValue": "{ans3}", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Solve for $x$ in the following, correct to 2 decimal places:&nbsp;</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"n10": {"definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "n10", "description": ""}, "ans1": {"definition": "e^(n3/n1)/n2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "ans2": {"definition": "e^(n7/n4)*(n6/n5)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "ans3": {"definition": "n9/(n10*(e^n8))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3", "description": ""}, "n8": {"definition": "random(5.5..8.5#0.1 except [7,8])", "templateType": "anything", "group": "Ungrouped variables", "name": "n8", "description": ""}, "n9": {"definition": "random(3.5..5.4#0.1 except [4,5])", "templateType": "anything", "group": "Ungrouped variables", "name": "n9", "description": ""}, "n1": {"definition": "random(7..11)", "templateType": "anything", "group": "Ungrouped variables", "name": "n1", "description": ""}, "n2": {"definition": "random(n1+1..21)", "templateType": "anything", "group": "Ungrouped variables", "name": "n2", "description": ""}, "n3": {"definition": "random(n2..40)", "templateType": "anything", "group": "Ungrouped variables", "name": "n3", "description": ""}, "n4": {"definition": "random(7.1..8.9#0.1 except 8)", "templateType": "anything", "group": "Ungrouped variables", "name": "n4", "description": ""}, "n5": {"definition": "random(2.5..5.5#0.1)", "templateType": "anything", "group": "Ungrouped variables", "name": "n5", "description": ""}, "n6": {"definition": "random(6..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "n6", "description": ""}, "n7": {"definition": "random(5.1..6.9#0.1 except 6)", "templateType": "anything", "group": "Ungrouped variables", "name": "n7", "description": ""}}, "metadata": {"notes": "<p>rebelmaths rebel Rebel REBEL</p>", "description": "<p>Using e to solve equations involving the natural log</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}]}]}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}]}