Precalculus Examples

$\ln (10^{x - 2})$

Step 1

Expand $\ln (10^{x - 2})$ by moving $x - 2$ outside the logarithm.

$(x - 2) \ln (10)$

Step 2

Rewrite $\ln (10)$ as $\ln (2 (5))$ .

$(x - 2) \ln (2 (5))$

Step 3

Rewrite $\ln (2 (5))$ as $\ln (2) + \ln (5)$ .

$(x - 2) (\ln (2) + \ln (5))$

Step 4

Expand $(x - 2) (\ln (2) + \ln (5))$ using the FOIL Method.

Tap for more steps...

Step 4.1

Apply the distributive property.

$x (\ln (2) + \ln (5)) - 2 (\ln (2) + \ln (5))$

Step 4.2

Apply the distributive property.

$x \ln (2) + x \ln (5) - 2 (\ln (2) + \ln (5))$

Step 4.3

Apply the distributive property.

$x \ln (2) + x \ln (5) - 2 \ln (2) - 2 \ln (5)$