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{"name": "Maria's copy of Using Laws for Addition and Subtraction of Logarithms", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"ungrouped_variables": ["x1", "y1"], "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "", "metadata": {"description": "<p>Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "rulesets": {}, "functions": {}, "name": "Maria's copy of Using Laws for Addition and Subtraction of Logarithms", "preamble": {"css": "", "js": ""}, "variable_groups": [], "tags": [], "variables": {"x1": {"group": "Ungrouped variables", "name": "x1", "definition": "repeat(random(2..5),8)", "templateType": "anything", "description": ""}, "y1": {"group": "Ungrouped variables", "name": "y1", "definition": "random(2..4)", "templateType": "anything", "description": ""}}, "parts": [{"showCorrectAnswer": true, "steps": [{"showCorrectAnswer": true, "customName": "", "type": "information", "variableReplacements": [], "customMarkingAlgorithm": "", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "unitTests": [], "scripts": {}, "useCustomName": false, "variableReplacementStrategy": "originalfirst", "prompt": "<p>When adding and subtracting logarithms we can simplify the expressions using some logarithm laws. These laws are</p>\n<p>\\[\\begin{align}<br/>\\log_a(x)+\\log_a(y)&amp;=\\log_a(xy)\\text{,}\\\\<br/>\\log_a(x)-\\log_a(y)&amp;=\\log_a\\left(\\frac{x}{y}\\right)\\text{.}<br/>\\end{align}\\]</p>", "marks": 0}], "customName": "", "type": "gapfill", "variableReplacements": [], "customMarkingAlgorithm": "", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "unitTests": [], "sortAnswers": false, "stepsPenalty": 0, "scripts": {}, "useCustomName": false, "gaps": [{"showCorrectAnswer": true, "showFractionHint": true, "customName": "", "type": "numberentry", "allowFractions": false, "variableReplacements": [], "customMarkingAlgorithm": "", "minValue": "x1[1]*x1[0]", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "unitTests": [], "mustBeReduced": false, "correctAnswerStyle": "plain", "correctAnswerFraction": false, "scripts": {}, "useCustomName": false, "maxValue": "x1[1]*x1[0]", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "marks": "0.5"}], "variableReplacementStrategy": "originalfirst", "prompt": "<p>$\\log_a(\\var{x1[1]})+ \\log_a(\\var{x1[0]})=\\log_a($ [[0]]$)$</p>", "marks": 0}, {"showCorrectAnswer": true, "steps": [{"showCorrectAnswer": true, "customName": "", "type": "information", "variableReplacements": [], "customMarkingAlgorithm": "", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "unitTests": [], "scripts": {}, "useCustomName": false, "variableReplacementStrategy": "originalfirst", "prompt": "<p>When adding and subtracting logarithms we can simplify the expressions using some logarithm laws. These laws are</p>\n<p>\\[\\begin{align}<br/>\\log_a(x)+\\log_a(y)&amp;=\\log_a(xy)\\text{,}\\\\<br/>\\log_a(x)-\\log_a(y)&amp;=\\log_a\\left(\\frac{x}{y}\\right)\\text{.}<br/>\\end{align}\\]</p>", "marks": 0}], "customName": "", "type": "gapfill", "variableReplacements": [], "customMarkingAlgorithm": "", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "unitTests": [], "sortAnswers": false, "stepsPenalty": 0, "scripts": {}, "useCustomName": false, "gaps": [{"showCorrectAnswer": true, "showFractionHint": true, "customName": "", "type": "numberentry", "allowFractions": false, "variableReplacements": [], "customMarkingAlgorithm": "", "minValue": "y1", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "unitTests": [], "mustBeReduced": false, "correctAnswerStyle": "plain", "correctAnswerFraction": false, "scripts": {}, "useCustomName": false, "maxValue": "y1", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "marks": "0.5"}], "variableReplacementStrategy": "originalfirst", "prompt": "<p>$\\log_a(\\var{(x1[4])*y1})-\\log_a(\\var{x1[4]})=\\log_a($ [[0]]$)$</p>", "marks": 0}], "statement": "<p>Simplify the expressions to fill in the gaps.</p>", "extensions": [], "type": "question", "contributors": [{"name": "Aiden McCall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1592/"}, {"name": "Hannah Aldous", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1594/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}]}], "contributors": [{"name": "Aiden McCall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1592/"}, {"name": "Hannah Aldous", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1594/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}