Precalculus Examples

$2 \log (p) \cdot (3 \log (q))$

Step 1

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

$\log (p^{2}) \cdot (3 \log (q))$

Step 2

Rewrite using the commutative property of multiplication.

$3 \log (p^{2}) \log (q)$

Step 3

Simplify $3 \log (p^{2})$ by moving $3$ inside the logarithm.

$\log ({(p^{2})}^{3}) \log (q)$

Step 4

Multiply the exponents in ${(p^{2})}^{3}$ .

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Step 4.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\log (p^{2 \cdot 3}) \log (q)$

Step 4.2

Multiply $2$ by $3$ .

$\log (p^{6}) \log (q)$