Calculus Examples

$\log_{x} (3 x y^{2})$

Step 1

Rewrite $\log_{x} (3 x y^{2})$ as $\log_{x} (3 x) + \log_{x} (y^{2})$ .

$\log_{x} (3 x) + \log_{x} (y^{2})$

Step 2

Rewrite $\log_{x} (3 x)$ as $\log_{x} (3) + \log_{x} (x)$ .

$\log_{x} (3) + \log_{x} (x) + \log_{x} (y^{2})$

Step 3

Expand $\log_{x} (y^{2})$ by moving $2$ outside the logarithm.

$\log_{x} (3) + \log_{x} (x) + 2 \log_{x} (y)$

Step 4

Logarithm base $x$ of $x$ is $1$ .

$\log_{x} (3) + 1 + 2 \log_{x} (y)$