// Numbas version: exam_results_page_options
{"name": "Logs: resulting in negatives", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": ""}, "statement": "<p>The following should be completed without the use of a calculator.</p>", "functions": {}, "tags": ["logarithms", "logs", "Logs", "negative indices", "negative powers"], "extensions": [], "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "", "variables": {"small": {"templateType": "anything", "definition": "random([2,3],[2,4],[3,3],[3,4],[4,3],[5,3])", "name": "small", "description": "", "group": "Ungrouped variables"}, "num1": {"templateType": "anything", "definition": "random(10..90)", "name": "num1", "description": "", "group": "Ungrouped variables"}, "num2": {"templateType": "anything", "definition": "random(2..12)", "name": "num2", "description": "", "group": "Ungrouped variables"}, "one": {"templateType": "anything", "definition": "random(map([b,1],b,list(2..12)))", "name": "one", "description": "", "group": "Ungrouped variables"}, "tens": {"templateType": "anything", "definition": "random([10,3],[10,4],[10,5],[10,6])", "name": "tens", "description": "", "group": "Ungrouped variables"}, "two": {"templateType": "anything", "definition": "random(map([b,2],b,list(2..12)))", "name": "two", "description": "", "group": "Ungrouped variables"}}, "ungrouped_variables": ["one", "two", "small", "tens", "num1", "num2"], "parts": [{"stepsPenalty": "2", "gaps": [{"correctAnswerFraction": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "maxValue": "1/{num1}", "mustBeReduced": false, "mustBeReducedPC": 0, "showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "allowFractions": true, "minValue": "1/{num1}", "correctAnswerStyle": "plain", "marks": 1, "scripts": {}, "type": "numberentry"}, {"correctAnswerFraction": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "maxValue": "1/{num2}^2", "mustBeReduced": false, "mustBeReducedPC": 0, "showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "allowFractions": true, "minValue": "1/{num2}^2", "correctAnswerStyle": "plain", "marks": 1, "scripts": {}, "type": "numberentry"}], "variableReplacementStrategy": "originalfirst", "steps": [{"variableReplacementStrategy": "originalfirst", "type": "information", "marks": 0, "variableReplacements": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "prompt": "<p>When learning index laws you would have seen that<br/>\\[x^{-n}=\\frac{1}{x^n}.\\]<br/><br/>Indices and logs are intimately related, ensure you revise your index laws.</p>", "scripts": {}}], "type": "gapfill", "marks": 0, "variableReplacements": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "prompt": "<p>Recall that we can convert negative indices to fractions</p>\n<p>$\\var{num1}^{-1}$ =&nbsp;[[0]]&nbsp;</p>\n<p>$\\var{num2}^{-2}$ =&nbsp;[[1]]&nbsp;</p>", "scripts": {}}, {"stepsPenalty": "1", "gaps": [{"correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "maxValue": "-1", "mustBeReduced": false, "mustBeReducedPC": 0, "showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "allowFractions": false, "minValue": "-1", "correctAnswerStyle": "plain", "marks": 1, "scripts": {}, "type": "numberentry"}], "variableReplacementStrategy": "originalfirst", "steps": [{"variableReplacementStrategy": "originalfirst", "type": "information", "marks": 0, "variableReplacements": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "prompt": "<p>To determine the value of $\\log_b(a)$, you can think \"$b$ to the what equals $a$\", and that will be your answer.</p>\n<p><br/>To determine $\\log_{\\var{one[0]}}\\left(\\frac{1}{\\var{one[0]}}\\right)$, realise $\\var{one[0]}^{-1}=\\frac{1}{\\var{one[0]}}$ and so $\\log_{\\var{one[0]}}\\left(\\frac{1}{\\var{one[0]}}\\right)=-1$.</p>", "scripts": {}}], "type": "gapfill", "marks": 0, "variableReplacements": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "prompt": "<p>Using the definition and your times tables determine the following:</p>\n<p>$\\log_{\\var{one[0]}}\\left(\\frac{1}{\\var{one[0]}}\\right)$ =&nbsp;[[0]]</p>", "scripts": {}}, {"stepsPenalty": "1", "gaps": [{"correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "maxValue": "-2", "mustBeReduced": false, "mustBeReducedPC": 0, "showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "allowFractions": false, "minValue": "-2", "correctAnswerStyle": "plain", "marks": 1, "scripts": {}, "type": "numberentry"}], "variableReplacementStrategy": "originalfirst", "steps": [{"variableReplacementStrategy": "originalfirst", "type": "information", "marks": 0, "variableReplacements": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "prompt": "<p>To determine the value of $\\log_b(a)$, you can think \"$b$ to the what equals $a$\", and that will be your answer.</p>\n<p><br/>To determine $\\log_{\\var{two[0]}}\\left(\\frac{1}{\\var{two[0]^2}}\\right)$, realise $\\var{two[0]}^{-2}=\\frac{1}{\\var{two[0]^2}}$ and so $\\log_{\\var{two[0]}}\\left(\\frac{1}{\\var{two[0]^2}}\\right)=-2$.</p>", "scripts": {}}], "type": "gapfill", "marks": 0, "variableReplacements": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "prompt": "<p>Using the definition and your times tables determine the following:</p>\n<p>$\\log_{\\var{two[0]}}\\left(\\frac{1}{\\var{two[0]^2}}\\right)$ =&nbsp;[[0]]</p>", "scripts": {}}, {"stepsPenalty": "1", "gaps": [{"correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "maxValue": "{-small[1]}", "mustBeReduced": false, "mustBeReducedPC": 0, "showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "allowFractions": false, "minValue": "{-small[1]}", "correctAnswerStyle": "plain", "marks": 1, "scripts": {}, "type": "numberentry"}], "variableReplacementStrategy": "originalfirst", "steps": [{"variableReplacementStrategy": "originalfirst", "type": "information", "marks": 0, "variableReplacements": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "prompt": "<p>To determine the value of $\\log_b(a)$, you can think \"$b$ to the what equals $a$\", and that will be your answer.</p>\n<p><br/>To determine $\\log_{\\var{small[0]}}\\left(\\frac{1}{\\var{small[0]^small[1]}}\\right)$, realise $\\var{small[0]}^{-\\var{small[1]}}=\\frac{1}{\\var{small[0]^small[1]}}$ and so $\\log_{\\var{small[0]}}\\left(\\frac{1}{\\var{small[0]^small[1]}}\\right)=-\\var{small[1]}$.</p>", "scripts": {}}], "type": "gapfill", "marks": 0, "variableReplacements": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "prompt": "<p>Using the definition and your times tables determine the following:</p>\n<p>$\\log_{\\var{small[0]}}\\left(\\frac{1}{\\var{small[0]^small[1]}}\\right)$ =&nbsp;[[0]]</p>", "scripts": {}}, {"stepsPenalty": "1", "gaps": [{"correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "maxValue": "{-tens[1]}", "mustBeReduced": false, "mustBeReducedPC": 0, "showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "allowFractions": false, "minValue": "{-tens[1]}", "correctAnswerStyle": "plain", "marks": 1, "scripts": {}, "type": "numberentry"}], "variableReplacementStrategy": "originalfirst", "steps": [{"variableReplacementStrategy": "originalfirst", "type": "information", "marks": 0, "variableReplacements": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "prompt": "<p>To determine the value of $\\log_b(a)$, you can think \"$b$ to the what equals $a$\", and that will be your answer.</p>\n<p><br/>To determine $\\log_{\\var{tens[0]}}(\\var{1/tens[0]^tens[1]})$, realise $\\var{tens[0]}^{-\\var{tens[1]}}=\\var{1/tens[0]^tens[1]}$ and so $\\log_{\\var{tens[0]}}(\\var{1/tens[0]^tens[1]})=-\\var{tens[1]}$.<br/><br/></p>\n<hr/>\n<p>Recall that $10^{-n}$ is the same as a decimal with zeros everywhere except a $1$ at the $n$th decimal place.</p>", "scripts": {}}], "type": "gapfill", "marks": 0, "variableReplacements": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "prompt": "<p>Using the definition and your times tables determine the following:</p>\n<p>$\\log_{\\var{tens[0]}}(\\var{1/tens[0]^tens[1]})$ =&nbsp;[[0]]</p>", "scripts": {}}], "preamble": {"css": "", "js": ""}, "name": "Logs: resulting in negatives", "variable_groups": [], "type": "question", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}