// Numbas version: exam_results_page_options {"name": "David's copy of Logs: resulting in negatives", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "parts": [{"steps": [{"scripts": {}, "variableReplacements": [], "prompt": "

When learning index laws you would have seen that
\\[x^{-n}=\\frac{1}{x^n}.\\]

Indices and logs are intimately related, ensure you revise your index laws.

", "showFeedbackIcon": true, "marks": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "information"}], "prompt": "

Recall that we can convert negative indices to fractions

$\\var{num1}^{-1}$ = [[0]]

$\\var{num2}^{-2}$ = [[1]]

", "stepsPenalty": "2", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "scripts": {}, "showFeedbackIcon": true, "marks": 0, "gaps": [{"mustBeReducedPC": 0, "variableReplacementStrategy": "originalfirst", "minValue": "1/{num1}", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": true, "maxValue": "1/{num1}", "variableReplacements": [], "scripts": {}, "showFeedbackIcon": true, "marks": 1, "mustBeReduced": false, "showCorrectAnswer": true, "correctAnswerStyle": "plain", "type": "numberentry", "allowFractions": true}, {"mustBeReducedPC": 0, "variableReplacementStrategy": "originalfirst", "minValue": "1/{num2}^2", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": true, "maxValue": "1/{num2}^2", "variableReplacements": [], "scripts": {}, "showFeedbackIcon": true, "marks": 1, "mustBeReduced": false, "showCorrectAnswer": true, "correctAnswerStyle": "plain", "type": "numberentry", "allowFractions": true}], "showCorrectAnswer": true, "type": "gapfill"}, {"steps": [{"scripts": {}, "variableReplacements": [], "prompt": "

To determine the value of $\\log_b(a)$, you can think \"$b$ to the what equals $a$\", and that will be your answer.

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 $\\log_{\\var{one[0]}}\\left(\\frac{1}{\\var{one[0]}}\\right)=-1$.

", "showFeedbackIcon": true, "marks": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "information"}], "prompt": "

Using the definition and your times tables determine the following:

$\\log_{\\var{one[0]}}\\left(\\frac{1}{\\var{one[0]}}\\right)$ = [[0]]

To determine the value of $\\log_b(a)$, you can think \"$b$ to the what equals $a$\", and that will be your answer.

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 $\\log_{\\var{two[0]}}\\left(\\frac{1}{\\var{two[0]^2}}\\right)=-2$.

", "showFeedbackIcon": true, "marks": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "information"}], "prompt": "

Using the definition and your times tables determine the following:

$\\log_{\\var{two[0]}}\\left(\\frac{1}{\\var{two[0]^2}}\\right)$ = [[0]]

To determine the value of $\\log_b(a)$, you can think \"$b$ to the what equals $a$\", and that will be your answer.

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 $\\log_{\\var{small[0]}}\\left(\\frac{1}{\\var{small[0]^small[1]}}\\right)=-\\var{small[1]}$.

", "showFeedbackIcon": true, "marks": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "information"}], "prompt": "

Using the definition and your times tables determine the following:

$\\log_{\\var{small[0]}}\\left(\\frac{1}{\\var{small[0]^small[1]}}\\right)$ = [[0]]

To determine the value of $\\log_b(a)$, you can think \"$b$ to the what equals $a$\", and that will be your answer.

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 $\\log_{\\var{tens[0]}}(\\var{1/tens[0]^tens[1]})=-\\var{tens[1]}$.

Recall that $10^{-n}$ is the same as a decimal with zeros everywhere except a $1$ at the $n$th decimal place.

", "showFeedbackIcon": true, "marks": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "information"}], "prompt": "

Using the definition and your times tables determine the following:

$\\log_{\\var{tens[0]}}(\\var{1/tens[0]^tens[1]})$ = [[0]]

", "stepsPenalty": "1", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "scripts": {}, "showFeedbackIcon": true, "marks": 0, "gaps": [{"mustBeReducedPC": 0, "variableReplacementStrategy": "originalfirst", "minValue": "{-tens[1]}", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "maxValue": "{-tens[1]}", "variableReplacements": [], "scripts": {}, "showFeedbackIcon": true, "marks": 1, "mustBeReduced": false, "showCorrectAnswer": true, "correctAnswerStyle": "plain", "type": "numberentry", "allowFractions": false}], "showCorrectAnswer": true, "type": "gapfill"}], "name": "David's copy of Logs: resulting in negatives", "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "rulesets": {}, "preamble": {"css": "", "js": ""}, "tags": ["logarithms", "logs", "Logs", "negative indices", "negative powers"], "ungrouped_variables": ["one", "two", "small", "tens", "num1", "num2"], "functions": {}, "extensions": [], "statement": "

The following should be completed without the use of a calculator.

", "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"small": {"group": "Ungrouped variables", "definition": "random([2,3],[2,4],[3,3],[3,4],[4,3],[5,3])", "templateType": "anything", "description": "", "name": "small"}, "num2": {"group": "Ungrouped variables", "definition": "random(2..12)", "templateType": "anything", "description": "", "name": "num2"}, "two": {"group": "Ungrouped variables", "definition": "random(map([b,2],b,list(2..12)))", "templateType": "anything", "description": "", "name": "two"}, "num1": {"group": "Ungrouped variables", "definition": "random(10..90)", "templateType": "anything", "description": "", "name": "num1"}, "one": {"group": "Ungrouped variables", "definition": "random(map([b,1],b,list(2..12)))", "templateType": "anything", "description": "", "name": "one"}, "tens": {"group": "Ungrouped variables", "definition": "random([10,3],[10,4],[10,5],[10,6])", "templateType": "anything", "description": "", "name": "tens"}}, "advice": "", "type": "question", "contributors": [{"name": "David Martin", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/130/"}, {"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "David Martin", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/130/"}, {"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}