Precalculus Examples

$\log (6) + 2 \log (4) + \log (32 + 4^{x})$

Step 1

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

$2 \log (4) + \log (6 (32 + 4^{x}))$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Simplify $2 \log (4)$ by moving $2$ inside the logarithm.

$\log (4^{2}) + \log (6 (32 + 4^{x}))$

Step 2.2

Raise $4$ to the power of $2$ .

$\log (16) + \log (6 (32 + 4^{x}))$

Step 2.3

Apply the distributive property.

$\log (16) + \log (6 \cdot 32 + 6 \cdot 4^{x})$

Step 2.4

Multiply $6$ by $32$ .

$\log (16) + \log (192 + 6 \cdot 4^{x})$

Step 3

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

$\log (16 (192 + 6 \cdot 4^{x}))$

Step 4

Apply the distributive property.

$\log (16 \cdot 192 + 16 (6 \cdot 4^{x}))$

Step 5

Multiply.

Tap for more steps...

Step 5.1

Multiply $16$ by $192$ .

$\log (3072 + 16 (6 \cdot 4^{x}))$

Step 5.2

Multiply $6$ by $16$ .

$\log (3072 + 96 \cdot 4^{x})$