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\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.
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"], "type": "1_n_2", "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:
", "minMarks": 0, "shuffleChoices": true}, {"variableReplacementStrategy": "originalfirst", "distractors": ["", "", "", "", "", ""], "steps": [{"variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "information", "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\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": [], "scripts": {}, "marks": 0}], "maxMarks": 0, "displayColumns": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "scripts": {}, "marks": 0, "displayType": "radiogroup", "stepsPenalty": "1", "matrix": ["1", 0, 0, 0, 0, 0], "choices": ["$\\log_x (z)=y$
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"], "type": "1_n_2", "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:
", "minMarks": 0, "shuffleChoices": true}, {"variableReplacementStrategy": "originalfirst", "steps": [{"variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "information", "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 $\\log_{\\var{zero[0]}}(\\var{zero[0]^zero[1]})=0$.
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 $\\log_{\\var{one[0]}}(\\var{one[0]^one[1]})$, 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$\\log_{\\var{one[0]}}(\\var{one[0]^one[1]})$ = [[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$\\log_{\\var{two[0]}}(\\var{two[0]^two[1]})$ = [[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$\\log_{\\var{small[0]}}(\\var{small[0]^small[1]})$ = [[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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\n$\\log_{\\var{tens[0]}}(\\var{tens[0]^tens[1]})$ = [[0]]
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