The compound interest formula is
$$ A =P( 1+r ) ^{n} $$
If I want to find $n$ it seems logical to that I just solve for it using the logarithm base (1+r), like so:
First divide by $P$:
$$ \dfrac{A}{P} = ( 1+r) ^{n} $$
and then:
$$ log_{(1+r)}(\dfrac{A}{P}) = n $$
which is easily solvable. However, this is wrong, apparently. It seems logical to me that you can just apply the rule that if $b^x=y$ then $log_{b}(y)=x$. Can somebody explain why this does not work? Thanks a lot!
EDIT: I made a mistake - I meant "solve for $n$", not "solve for $r$", as I wrote first. Sorry for the confusion!