Precalculus Examples

$\log (4^{2 x - 7})$

Step 1

Expand $\log (4^{2 x - 7})$ by moving $2 x - 7$ outside the logarithm.

$(2 x - 7) \log (4)$

Step 2

Rewrite $\log (4)$ as $\log (2^{2})$ .

$(2 x - 7) \log (2^{2})$

Step 3

Expand $\log (2^{2})$ by moving $2$ outside the logarithm.

$(2 x - 7) (2 \log (2))$

Step 4

Apply the distributive property.

$2 x (2 \log (2)) - 7 (2 \log (2))$

Step 5

Multiply $2$ by $2$ .

$4 x \log (2) - 7 (2 \log (2))$

Step 6

Multiply $2$ by $- 7$ .

$4 x \log (2) - 14 \log (2)$