Question

Let $\log \left(x\right)=3$ and $\log \left(y\right)=5$; Find $\log \left(x^{2}y\right)$

• A. $11$
• B. $14$
• C. $15$
• D. $28$
• E. $45$

Answer 1

The correct option is A $11$

Since $\log \left(xy\right)=\log \left(x\right)+\log \left(y\right)$ and $\log \left(x^2\right)=2\log \left(x\right)$

Therefore, $\log \left(x^{2}y\right)=\log \left(x^2\right)+\log \left(y\right)=2\log \left(x\right)+\log \left(y\right)$

It is given that $\log \left(x\right)=3$ and $\log \left(y\right)=5$, now $\log \left(x^{2}y\right)$ can be determined as:

$\log \left(x^{2}y\right)=2\log \left(x\right)+\log \left(y\right)=(2\times 3)+5=6+5=11$