Question

3=(1.02)^1t . I have the answer I just need to know the steps needed to solve the problem. I don't understand how to bring the t down.

Answer 1

take the log of both sides or natural log of both sides.

Answer 2

\[3=(1.02)^t\]
\[\ln(3)=t\times \ln(1.02)\]
\[t=\frac{\ln(3)}{\ln(1.02)}\]

Answer 3

if you need another step it is
\[\ln(3)=\ln((1.02)^t)=t\ln(1.02)\]

Answer 4

but that step ,while being correct, should be unnecessary because
\[b^x=e^{x\ln(b)}\]
so
\[(1.02)^t=e^{t\ln(1.02)}\] hence
\[\ln((1.02)^t)=t\ln(1.02)\]