Answer
(a) 25
(b) 3
(c) $\frac{4}{3}$
Work Step by Step
(a) $e^{2\ln 5}=e^{(\ln 5)\cdot 2}=(e^{\ln 5})^2=5^2=25$
(b) $\log_64+\log_654=\log_6(4\cdot 54)=\log_6216=\log_66^3=3$
(c)
Let $x=\arcsin \frac{4}{5}$.
We have $\sin (x)=4/5$ and so $\cos (x)=3/5$.
So, $\tan (\arcsin \frac{4}{5})=\tan (x)=\frac{\sin (x)}{\cos (x)}=\frac{4/5}{3/5}=\frac{4}{3}$
