A pretty good attempt, well done!
I prefer not to introduce the $\displaystyle \displaystyle \log$
$\displaystyle \displaystyle 25000 = 10000\left(1+\frac{R}{100}\right)^6$
$\displaystyle \displaystyle 2.5 =\left(1+\frac{R}{100}\right)^6$
$\displaystyle \displaystyle \sqrt[6]{2.5} =1+\frac{R}{100}$
$\displaystyle \displaystyle\sqrt[6]{2.5}-1 =\frac{R}{100}$
$\displaystyle \displaystyle 100(\sqrt[6]{2.5}-1) =R$
$\displaystyle \displaystyle 25000 = 10000\left(1+\frac{R}{100}\right)^{0.6}$
$\displaystyle \displaystyle 2.5 =\left(1+\frac{R}{100}\right)^{0.6}$
$\displaystyle \displaystyle (2.5)^{\frac{5}{3}} =1+\frac{R}{100}$
$\displaystyle \displaystyle (2.5)^{\frac{5}{3}}-1 =\frac{R}{100}$
$\displaystyle \displaystyle 100[(2.5)^{\frac{5}{3}}-1] =R$