Precalculus Examples

$\ln (| \sec (x) |) + \ln (| \sin (x) |)$

Step 1

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\ln (| \sec (x) | | \sin (x) |)$

Step 2

To multiply absolute values, multiply the terms inside each absolute value.

$\ln (| \sec (x) \sin (x) |)$

Step 3

Rewrite $\sec (x)$ in terms of sines and cosines.

$\ln (| \frac{1}{\cos (x)} \sin (x) |)$

Step 4

Combine $\frac{1}{\cos (x)}$ and $\sin (x)$ .

$\ln (| \frac{\sin (x)}{\cos (x)} |)$

Step 5

Convert from $\frac{\sin (x)}{\cos (x)}$ to $\tan (x)$ .

$\ln (| \tan (x) |)$