Question

I need to calculate X 2^x=200 Solve for x

Answer 1

Remember
$log(a^z)=zlog(a)$
so

notice that 200=2*2*2*5*5, so x cannot be a whole number

take the log base 10 of both sides

$log_{10}(2^x)=log{10}(200)$
$xlog_{10}(2)=log{10}(200)$
divide both sides by $log_{10}(2)$
$x= \frac{log_{10}(200)}{log_{10}(2)}$

if we used $log_{2}$ instead of $log_{10}$ we would get
$x= log_{2}(200)$ because $log_{a}(a^b)=b$