Find $\log_{p}X^2$?

Question

Given that $\log_{p}X=5$ and $\log_{p}Y=2$, find

i) $\log_{p}X^2$

I did this, $X=p^5$ and $Y=p^2$

But how do I use them? Should I find $p$?

Answer 1

Hint:
Just use the identity:

$$\log_{\,b}x^n=n\log_{\,b}x .$$

Answer 2

$\log_p X^2 = 2 \log_p X = 2 \cdot 5 = 10$.

Answer 3

$log_pX^2=log_p(p^5)^2=log_p(p^{10})=10$