Precalculus Examples

$\log (2) (8 x + 9)$

Step 1

Apply the distributive property.

$\log (2) (8 x) + \log (2) \cdot 9$

Step 2

Simplify $8 \log (2)$ by moving $8$ inside the logarithm.

$\log (2^{8}) x + \log (2) \cdot 9$

Step 3

Multiply $\log (2) \cdot 9$ .

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Step 3.1

Reorder $\log (2)$ and $9$ .

$\log (2^{8}) x + 9 \cdot \log (2)$

Step 3.2

Simplify $9 \cdot \log (2)$ by moving $9$ inside the logarithm.

$\log (2^{8}) x + \log (2^{9})$

Step 4

Simplify each term.

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Step 4.1

Raise $2$ to the power of $8$ .

$\log (256) x + \log (2^{9})$

Step 4.2

Raise $2$ to the power of $9$ .

$\log (256) x + \log (512)$

Step 5

Reorder factors in $\log (256) x + \log (512)$ .

$x \log (256) + \log (512)$