// Numbas version: exam_results_page_options
{"name": "Blathnaid's copy of Simplify logarithms", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"d": {"group": "Ungrouped variables", "definition": "s4*random(2..9)", "templateType": "anything", "name": "d", "description": ""}, "s4": {"group": "Ungrouped variables", "definition": "random(1,-1)", "templateType": "anything", "name": "s4", "description": ""}, "s1": {"group": "Ungrouped variables", "definition": "random(1,-1)", "templateType": "anything", "name": "s1", "description": ""}, "f": {"group": "Ungrouped variables", "definition": "precround((a2-1)/b2,0)", "templateType": "anything", "name": "f", "description": ""}, "a1": {"group": "Ungrouped variables", "definition": "s1*random(2..9)", "templateType": "anything", "name": "a1", "description": ""}, "b1": {"group": "Ungrouped variables", "definition": "random(2..15)", "templateType": "anything", "name": "b1", "description": ""}, "a2": {"group": "Ungrouped variables", "definition": "1+b2*random(2..5)", "templateType": "anything", "name": "a2", "description": ""}, "b2": {"group": "Ungrouped variables", "definition": "random(2..9)", "templateType": "anything", "name": "b2", "description": ""}, "c": {"group": "Ungrouped variables", "definition": "random(1..9)", "templateType": "anything", "name": "c", "description": ""}}, "name": "Blathnaid's copy of Simplify logarithms", "functions": {}, "tags": [], "metadata": {"description": "\n            \t\t<p>Express&nbsp;$\\log_a(x^{c}y^{d})$&nbsp;in terms of $\\log_a(x)$ and $\\log_a(y)$. Find $q(x)$ such that $\\frac{f}{g}\\log_a(x)+\\log_a(rx+s)-\\log_a(x^{1/t})=\\log_a(q(x))$</p>\n            \t\t    <p>&nbsp;</p>\n            \t\t", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Find $\\alpha$ and $\\beta$.</p>\n<p></p>", "extensions": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "ungrouped_variables": ["c", "d", "f", "s1", "s4", "a1", "a2", "b1", "b2"], "preamble": {"js": "", "css": ""}, "variable_groups": [], "advice": "<p>The rules for combining logs are</p>\n  <p>\\[\\begin{eqnarray*} \\log_a(bc)&amp;=&amp;\\log_a(b)+\\log_a(c)\\\\ \\\\ \\log_a\\left(\\frac{b}{c}\\right)&amp;=&amp;\\log_a(b)-\\log_a(c)\\\\ \\\\ \\log_a(b^r)&amp;=&amp;r\\log_a(b) \\end{eqnarray*} \\]</p>\n  <p>a)<br/>Using these rules gives:<br/>\\[ \\begin{eqnarray*} \\log_a(x^{\\var{a1}}y^{\\var{b1}})&amp;=&amp;\\log_a(x^{\\var{a1}})+\\log_a(y^{\\var{b1}})\\\\ &amp;=&amp;\\var{a1}\\log_a(x)+\\var{b1}\\log_a(y) \\end{eqnarray*} \\]</p>\n  <p>b)<br/>\\[\\begin{eqnarray*} \\simplify[std]{{a2}/{b2}}\\log_a(x)+\\log_a(\\simplify{{c}*x+{d}})-\\log_a(\\simplify{x^(1/{b2})})&amp;=&amp;\\log_a(x^\\frac{\\var{a2}}{\\var{b2}})+\\log_a(\\simplify{{c}*x+{d}})-\\log_a(\\simplify{x^(1/{b2})})\\\\ \\\\ &amp;=&amp;\\log_a\\left(\\simplify[std]{(x^({a2}/{b2})*({c}x+{d}))/(x^(1/{b2}))}\\right)\\\\ &amp;=&amp;\\log_a\\left(\\simplify{x^{f}*({c}x+{d})}\\right) \\end{eqnarray*} \\]</p>", "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "parts": [{"customName": "", "variableReplacements": [], "adaptiveMarkingPenalty": 0, "showFeedbackIcon": true, "useCustomName": false, "unitTests": [], "showCorrectAnswer": true, "gaps": [{"customName": "", "minValue": "{a1}", "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "notationStyles": ["plain", "en", "si-en"], "useCustomName": false, "variableReplacements": [], "scripts": {}, "allowFractions": false, "correctAnswerFraction": false, "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "maxValue": "{a1}", "mustBeReduced": false, "showFractionHint": true, "unitTests": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": 0.5, "correctAnswerStyle": "plain", "type": "numberentry", "variableReplacementStrategy": "originalfirst"}, {"customName": "", "minValue": "{b1}", "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "notationStyles": ["plain", "en", "si-en"], "useCustomName": false, "variableReplacements": [], "scripts": {}, "allowFractions": false, "correctAnswerFraction": false, "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "maxValue": "{b1}", "mustBeReduced": false, "showFractionHint": true, "unitTests": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": 0.5, "correctAnswerStyle": "plain", "type": "numberentry", "variableReplacementStrategy": "originalfirst"}], "marks": 0, "sortAnswers": false, "prompt": "<p></p>\n<p>\\[\\log_a(x^{\\var{a1}}y^{\\var{b1}})=\\alpha\\log_a(x)+\\beta\\log_a(y)\\]</p>\n<p>$\\alpha=\\;\\;$[[0]], $\\beta=\\;\\;$[[1]]</p>", "scripts": {}, "type": "gapfill", "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true}], "contributors": [{"name": "Blathnaid Sheridan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/447/"}, {"name": "Ida Landg\u00e4rds", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2336/"}]}]}], "contributors": [{"name": "Blathnaid Sheridan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/447/"}, {"name": "Ida Landg\u00e4rds", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2336/"}]}