// 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:
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\n\nThis 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:
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\n\nThis 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]]
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\n
To determine $\\log_{\\var{zero[0]}}(\\var{zero[0]^zero[1]})$, realise $\\var{zero[0]}^0=\\var{zero[0]^zero[1]}$ and so $\\log_{\\var{zero[0]}}(\\var{zero[0]^zero[1]})=0$.
Using the definition and your times tables determine the following:
\n$\\log_{\\var{one[0]}}(\\var{one[0]^one[1]})$ = [[0]]
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\n
To determine $\\log_{\\var{one[0]}}(\\var{one[0]^one[1]})$, realise $\\var{one[0]}^1=\\var{one[0]}$ and so $\\log_{\\var{one[0]}}(\\var{one[0]^one[1]})=1$.
Using the definition and your times tables determine the following:
\n$\\log_{\\var{two[0]}}(\\var{two[0]^two[1]})$ = [[0]]
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\n
To determine $\\log_{\\var{two[0]}}(\\var{two[0]^two[1]})$, realise $\\var{two[0]}^2=\\var{two[0]^2}$ and so $\\log_{\\var{two[0]}}(\\var{two[0]^two[1]})=2$.
Using the definition and your times tables determine the following:
\n$\\log_{\\var{small[0]}}(\\var{small[0]^small[1]})$ = [[0]]
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\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 $\\log_{\\var{small[0]}}(\\var{small[0]^small[1]})=\\var{small[1]}$.
Using the definition and your times tables determine the following:
\n$\\log_{\\var{tens[0]}}(\\var{tens[0]^tens[1]})$ = [[0]]
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\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 $\\log_{\\var{tens[0]}}(\\var{tens[0]^tens[1]})=\\var{tens[1]}$.
Recall that $10^n$ is the same as a $1$ with $n$ zeros behind it.
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