How would I rewrite this logarithmic equation: $\ln(37)= 3.6109$, in exponential form?
-Thanks
$\endgroup$ 72 Answers
$\begingroup$The definition of $\ln(x)$ is that it is the number $y$ such that $e^y=x$. In other words, $$e^{\ln(x)}=x.$$ We have the equation $$\ln(37)=3.6109.$$ Because both sides are equal, we have that $$e^{\ln(37)}=e^{3.6109}.$$ By the definition of $\ln$, this simplifies to $$37=e^{3.6109}.$$
$\endgroup$ 0 $\begingroup$Another way to see it (that is equivalent to Zev's answer) is that
$\log_{b}(a) = x$
is equivalent to
$a = b^x$.
$\ln$ is just $\log_{e}$, so
$\ln(37) = 3.6109$
is simply $\log_b(a) = x$ with
$b = e$, $a = 37$, $x = 3.6109$
and can be rewritten as
$37 = e^{3.6109}$.
That good enough for your needs?
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