Precalculus Examples

$\log (A) + 3 \log (2 B)$

Step 1

Simplify each term.

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Step 1.1

Simplify $3 \log (2 B)$ by moving $3$ inside the logarithm.

$\log (A) + \log ({(2 B)}^{3})$

Step 1.2

Apply the product rule to $2 B$ .

$\log (A) + \log (2^{3} B^{3})$

Step 1.3

Raise $2$ to the power of $3$ .

$\log (A) + \log (8 B^{3})$

Step 2

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

$\log (A (8 B^{3}))$

Step 3

Rewrite using the commutative property of multiplication.

$\log (8 A B^{3})$