// Numbas version: finer_feedback_settings
{"name": "Logarithms", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Logarithms", "tags": [], "metadata": {"description": "\n            \t\t<p>Express&nbsp;$\\log_a(x^{c}y^{d})$&nbsp;in terms of $\\log_a(x)$ and $\\log_a(y)$.&nbsp;</p>\n            \t\t    <p>&nbsp;</p>\n            \t\t", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Answer the following question on logarithms.</p>", "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><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>", "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"a1": {"name": "a1", "group": "Ungrouped variables", "definition": "s1*random(2..9)", "description": "", "templateType": "anything", "can_override": false}, "b1": {"name": "b1", "group": "Ungrouped variables", "definition": "random(2..15)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "s1": {"name": "s1", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "s4*random(2..9)", "description": "", "templateType": "anything", "can_override": false}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "precround((a2-1)/b2,0)", "description": "", "templateType": "anything", "can_override": false}, "s4": {"name": "s4", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything", "can_override": false}, "a2": {"name": "a2", "group": "Ungrouped variables", "definition": "1+b2*random(2..5)", "description": "", "templateType": "anything", "can_override": false}, "b2": {"name": "b2", "group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["c", "d", "f", "s1", "s4", "a1", "a2", "b1", "b2"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "\n      <p>Express the following in terms of $\\log_a(x)$ and $\\log_a(y)$</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>\n      ", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 0.5, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], 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