// Numbas version: exam_results_page_options
{"name": "Jeanne'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": [{"advice": "<h4>a)</h4>\n<p>We need to use the rule</p>\n<p>\\[\\log_a(x)+\\log_a(y)=\\log_a(xy)\\text{.}\\]</p>\n<p>Substituting in our values for $x$ and $y$ gives</p>\n<p>\\[\\begin{align}<br/>\\log_a(\\var{x1[1]})+\\log_a(\\var{x1[0]})&amp;=\\log_a(\\var{x1[1]}\\times \\var{x1[0]})\\\\<br/>&amp;=\\log_a(\\var{x1[1]*x1[0]})\\text{.}<br/>\\end{align}\\]</p>\n<p><em></em></p>\n<h4>b)</h4>\n<p>We need to use the rule</p>\n<p>\\[\\log_a(x)-\\log_a(y)=\\log_a\\left(\\frac{x}{y}\\right)\\text{.}\\]</p>\n<p>Substituting in our values for $x$ and $y$ gives</p>\n<p>\\[\\begin{align}<br/>\\log_a(\\var{x1[4]*y1})-\\log_a(\\var{x1[4]})&amp;=\\log_a(\\var{x1[4]*y1}\\div \\var{x1[4]})\\\\<br/>&amp;=\\log_a(\\var{y1})\\text{.}<br/>\\end{align}\\]</p>\n<h4><em></em><em></em></h4>", "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"}, "functions": {}, "variable_groups": [], "preamble": {"js": "", "css": ""}, "rulesets": {}, "statement": "<p>Simplifier les expressions suivantes</p>", "tags": [], "extensions": [], "ungrouped_variables": ["x1", "y1"], "name": "Jeanne's copy of Using Laws for Addition and Subtraction of Logarithms", "variablesTest": {"condition": "", "maxRuns": 100}, "variables": {"y1": {"description": "", "templateType": "anything", "name": "y1", "group": "Ungrouped variables", "definition": "random(2..6)"}, "x1": {"description": "", "templateType": "anything", "name": "x1", "group": "Ungrouped variables", "definition": "repeat(random(2..20),8)"}}, "parts": [{"stepsPenalty": 0, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "gaps": [{"maxValue": "x1[1]*x1[0]", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "minValue": "x1[1]*x1[0]", "scripts": {}, "correctAnswerFraction": false, "allowFractions": false, "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "marks": "2", "customMarkingAlgorithm": "", "type": "numberentry", "unitTests": [], "mustBeReducedPC": 0, "showCorrectAnswer": true, "mustBeReduced": false, "extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain"}], "scripts": {}, "showFeedbackIcon": true, "steps": [{"marks": 0, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "information", "unitTests": [], "scripts": {}, "showCorrectAnswer": true, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "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, "sortAnswers": false, "customMarkingAlgorithm": "", "type": "gapfill", "unitTests": [], "showCorrectAnswer": true, "prompt": "<p>$\\ln(\\var{x1[1]})+ \\ln(\\var{x1[0]})=\\ln($ [[0]]$)$</p>", "extendBaseMarkingAlgorithm": true}, {"stepsPenalty": 0, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "gaps": [{"maxValue": "y1", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "minValue": "y1", "scripts": {}, "correctAnswerFraction": false, "allowFractions": false, "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "marks": "2", "customMarkingAlgorithm": "", "type": "numberentry", "unitTests": [], "mustBeReducedPC": 0, "showCorrectAnswer": true, "mustBeReduced": false, "extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain"}], "scripts": {}, "showFeedbackIcon": true, "steps": [{"marks": 0, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "information", "unitTests": [], "scripts": {}, "showCorrectAnswer": true, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "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, "sortAnswers": false, "customMarkingAlgorithm": "", "type": "gapfill", "unitTests": [], "showCorrectAnswer": true, "prompt": "<p>$\\log_a(\\var{(x1[4])*y1})-\\log_a(\\var{x1[4]})=\\log_a($ [[0]]$)$</p>", "extendBaseMarkingAlgorithm": true}], "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": "Jeanne Parmentier", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2126/"}]}]}], "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": "Jeanne Parmentier", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2126/"}]}