$$\log(\frac{5^{2}t^{5}a^{2}}{\sqrt{4\cdot4+b^{3}}})$$
$\log(e)\left(\ln(\frac{a^{2}t^{5}}{\sqrt{b^{3}+16}})+2\ln(5)\right)$
$\frac{5\log(e)}{t}$
