$5-3.($Compound value solving for n$)$ How many years will the following take?

a$.$ $$500$ to grow to $$1,039\mathrm{.}50$ if invested at $5$ percent compounded annually

b$.$ $$35$ to grow to $$53\mathrm{.}87$ if invested at $9$ percent compounded annually

c$.$ $$100$ to grow to $$298\mathrm{.}60$ if invested at $20$ percent compounded annually

d$.$ $$53$ to grow to $$78\mathrm{.}76$ if invested at $2$ percent compounded annually