Question 840597
Find the logarithm of each side of the equation; do so symbolically first.  Substitute the values later.


You will want the rate as a decimal fraction, but this solution is adjusted for keeping r as you gave it, as a decimal value as a percent quantity.
{{{A=P(1+r/(100n))^(nt)}}}.
{{{ln(A)=ln(P)+ln((1+r/(100n))^(nt))}}}
{{{ln(A)-ln(P)=nt*ln((1+r/(100n)))}}}
{{{highlight(t=(ln(A)-ln(P))/(n*ln(1+r/(100n))))}}}
I chose natural logarithm, but you could just as well choose base ten or common logarithm.