// Numbas version: exam_results_page_options {"name": "Nuala's copy of Logs: definition and concrete numbers", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["zero", "one", "two", "small", "tens"], "name": "Nuala's copy of Logs: definition and concrete numbers", "tags": ["logarithms", "logs"], "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": 0, "displayColumns": 0, "variableReplacements": [], "prompt": "

The definition of a logarithm says if $b$ and $a$ are positive and $b$ is not equal to 1, then  $\\log_b(a)=c$ is equivalent to:

", "matrix": ["1", 0, 0, 0, 0, 0], "shuffleChoices": true, "distractors": ["", "", "", "", "", ""], "choices": ["

$b^c=a$

", "

$b^a=c$

", "

$a^b=c$

", "

$a^c=b$

", "

$c^a=b$

", "

$c^b=a$

"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": 0, "scripts": {}, "marks": 0, "steps": [{"prompt": "

The definition of a logarithm says if $b$ and $a$ are positive and $b$ is not equal to 1, then  $\\log_b(a)=c$ is equivalent to $b^c=a$.

\n

\n

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

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}, {"stepsPenalty": 0, "displayColumns": 0, "variableReplacements": [], "prompt": "

The definition of a logarithm says that if $x$ and $z$ are positive and $x$ is not equal to 1, then $x^y=z$ is equivalent to:

", "matrix": ["1", 0, 0, 0, 0, 0], "shuffleChoices": true, "distractors": ["", "", "", "", "", ""], "choices": ["

$\\log_x (z)=y$

", "

$\\log_x (y)=z$

", "

$\\log_y (x)=z$

", "

$\\log_y (z)=x$

", "

$\\log_z (y)=x$

", "

$\\log_z (x)=y$

"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": 0, "scripts": {}, "marks": 0, "steps": [{"prompt": "

The definition of a logarithm says if $b$ and $a$ are positive and $b$ is not equal to 1, then  $\\log_b(a)=c$ is equivalent to $b^c=a$.

\n

\n

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

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}, {"stepsPenalty": 0, "prompt": "

Using the definition and your times tables determine the following:

\n

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

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{zero[1]}", "minValue": "{zero[1]}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "

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

\n


To determine $\\log_{\\var{zero[0]}}(\\var{zero[0]^zero[1]})$, realise $\\var{zero[0]}^0=\\var{zero[0]^zero[1]}$ and so $\\log_{\\var{zero[0]}}(\\var{zero[0]^zero[1]})=0$.

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "

Using the definition and your times tables determine the following:

\n

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

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{one[1]}", "minValue": "{one[1]}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "

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

\n


To determine $\\log_{\\var{one[0]}}(\\var{one[0]^one[1]})$, realise $\\var{one[0]}^1=\\var{one[0]}$ and so $\\log_{\\var{one[0]}}(\\var{one[0]^one[1]})=1$.

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "

Using the definition and your times tables determine the following:

\n

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

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{two[1]}", "minValue": "{two[1]}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "

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

\n


To determine $\\log_{\\var{two[0]}}(\\var{two[0]^two[1]})$, realise $\\var{two[0]}^2=\\var{two[0]^2}$ and so $\\log_{\\var{two[0]}}(\\var{two[0]^two[1]})=2$.

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "

Using the definition and your times tables determine the following:

\n

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

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{small[1]}", "minValue": "{small[1]}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "

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

\n


To determine $\\log_{\\var{small[0]}}(\\var{small[0]^small[1]})$, realise $\\var{small[0]}^\\var{small[1]}=\\var{small[0]^small[1]}$ and so $\\log_{\\var{small[0]}}(\\var{small[0]^small[1]})=\\var{small[1]}$.

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "

Using the definition and your times tables determine the following:

\n

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

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{tens[1]}", "minValue": "{tens[1]}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "

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

\n


To determine $\\log_{\\var{tens[0]}}(\\var{tens[0]^tens[1]})$, realise $\\var{tens[0]}^\\var{tens[1]}=\\var{tens[0]^tens[1]}$ and so $\\log_{\\var{tens[0]}}(\\var{tens[0]^tens[1]})=\\var{tens[1]}$.

\n
\n

Recall that $10^n$ is the same as a $1$ with $n$ zeros behind it.

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}], "statement": "

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

", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"small": {"definition": "random([2,3],[2,4],[3,3],[3,4],[4,3],[5,3])", "templateType": "anything", "group": "Ungrouped variables", "name": "small", "description": ""}, "tens": {"definition": "random([10,3],[10,4],[10,5],[10,6])", "templateType": "anything", "group": "Ungrouped variables", "name": "tens", "description": ""}, "zero": {"definition": "random(map([b,0],b,list(2..12)))", "templateType": "anything", "group": "Ungrouped variables", "name": "zero", "description": ""}, "two": {"definition": "random(map([b,2],b,list(2..12)))", "templateType": "anything", "group": "Ungrouped variables", "name": "two", "description": ""}, "one": {"definition": "random(map([b,1],b,list(2..12)))", "templateType": "anything", "group": "Ungrouped variables", "name": "one", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Nuala Davis", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/821/"}]}]}], "contributors": [{"name": "Nuala Davis", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/821/"}]}