// Numbas version: finer_feedback_settings {"name": "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": {}, "advice": "", "ungrouped_variables": ["zero", "one", "two", "small", "tens"], "variable_groups": [], "preamble": {"css": "", "js": ""}, "tags": ["logarithms", "logs"], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "rulesets": {}, "variables": {"two": {"description": "", "definition": "random(map([b,2],b,list(2..12)))", "templateType": "anything", "name": "two", "group": "Ungrouped variables"}, "zero": {"description": "", "definition": "random(map([b,0],b,list(2..12)))", "templateType": "anything", "name": "zero", "group": "Ungrouped variables"}, "one": {"description": "", "definition": "random(map([b,1],b,list(2..12)))", "templateType": "anything", "name": "one", "group": "Ungrouped variables"}, "small": {"description": "", "definition": "random([2,3],[2,4],[3,3],[3,4],[4,3],[5,3])", "templateType": "anything", "name": "small", "group": "Ungrouped variables"}, "tens": {"description": "", "definition": "random([10,3],[10,4],[10,5],[10,6])", "templateType": "anything", "name": "tens", "group": "Ungrouped variables"}}, "name": "Logs: definition and concrete numbers", "statement": "

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

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$b^c=a$

", "

$b^a=c$

", "

$a^b=c$

", "

$a^c=b$

", "

$c^a=b$

", "

$c^b=a$

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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:

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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 $b^c=a$.

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.

$\\log_x (z)=y$

", "

$\\log_x (y)=z$

", "

$\\log_y (x)=z$

", "

$\\log_y (z)=x$

", "

$\\log_z (y)=x$

", "

$\\log_z (x)=y$

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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:

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 $b^c=a$.

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.

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

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Using the definition and your times tables determine the following:

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

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

", "variableReplacementStrategy": "originalfirst", "scripts": {}, "variableReplacements": []}], "prompt": "

Using the definition and your times tables determine the following:

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

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

", "variableReplacementStrategy": "originalfirst", "scripts": {}, "variableReplacements": []}], "prompt": "

Using the definition and your times tables determine the following:

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

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

", "variableReplacementStrategy": "originalfirst", "scripts": {}, "variableReplacements": []}], "prompt": "

Using the definition and your times tables determine the following:

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

", "variableReplacementStrategy": "originalfirst", "scripts": {}, "variableReplacements": []}, {"gaps": [{"mustBeReduced": false, "marks": 1, "mustBeReducedPC": 0, "allowFractions": false, "correctAnswerFraction": false, "minValue": "{tens[1]}", "maxValue": "{tens[1]}", "scripts": {}, "variableReplacements": [], "type": "numberentry", "showFeedbackIcon": true, "showCorrectAnswer": true, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst"}], "type": "gapfill", "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": 0, "stepsPenalty": "1", "steps": [{"type": "information", "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": 0, "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 $\\log_{\\var{tens[0]}}(\\var{tens[0]^tens[1]})$, realise $\\var{tens[0]}^\\var{tens[1]}=\\var{tens[0]^tens[1]}$ and so $\\log_{\\var{tens[0]}}(\\var{tens[0]^tens[1]})=\\var{tens[1]}$.

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

", "variableReplacementStrategy": "originalfirst", "scripts": {}, "variableReplacements": []}], "prompt": "

Using the definition and your times tables determine the following:

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

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