In this question we are using the change of base rule:
\n\\[\\log_b(a)=\\frac{\\log_c(a)}{\\log_c(b)}\\]
\nNotice, $c$ can be any base. Also, notice the big $a$ goes at the top of the fraction, and the little $b$ goes down the bottom.
", "showCorrectAnswer": true, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true}], "unitTests": [], "showFeedbackIcon": true, "prompt": "$\\ln(x)$ is the natural logarithm of $x$, or the log of $x$ base $e$. This is equivalent to $\\log_e(x)$ but $\\ln(x)$ is normally preferred, in fact, for this question it is required.
\n
$\\log_{\\var{base1}}(\\var{arg1})$ can be written in terms of natural logarithms as [[0]].
Note: The natural log is denoted by ln, that is, an L (in lower case) followed by an n, the first letter is not a capital i. To enter your answer ensure you use the correct letters and use brackets.
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\n\\[\\log_b(a)=\\frac{\\log_c(a)}{\\log_c(b)}\\]
\nNotice, $c$ can be any base. Also, notice the big $a$ goes at the top of the fraction, and the little $b$ goes down the bottom.
", "showCorrectAnswer": true, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true}], "unitTests": [], "showFeedbackIcon": true, "prompt": "The expression $\\displaystyle\\frac{\\log_\\var{base2}(\\var{num})}{\\log_\\var{base2}(\\var{den})}$ can be written as
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", "$\\log_{\\var{num}}(\\var{den})$
", "$\\log_{\\var{base2}}(\\var{num-den})$
", "$\\log_{\\var{base2}}\\left(\\frac{\\var{num}}{\\var{den}}\\right)$
", "$\\log_{\\var{den}}(\\var{base2})$
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