Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

$\ln (\tan (x))$