How would I rewrite this logarithmic equation: $\ln(37)= 3.6109$, in exponential form?
-Thanks
How would I rewrite this logarithmic equation: $\ln(37)= 3.6109$, in exponential form?
-Thanks
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 $37=e^{3.6109}.$
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?