Precalculus Examples

$4 \log_{3} (a) \cdot (3 \log_{3} (2 b)) - \log_{3} (m)$

Step 1

Simplify $4 \log_{3} (a)$ by moving $4$ inside the logarithm.

$\log_{3} (a^{4}) \cdot (3 \log_{3} (2 b)) - \log_{3} (m)$

Step 2

Rewrite using the commutative property of multiplication.

$3 \log_{3} (a^{4}) \log_{3} (2 b) - \log_{3} (m)$

Step 3

Simplify $3 \log_{3} (a^{4})$ by moving $3$ inside the logarithm.

$\log_{3} ({(a^{4})}^{3}) \log_{3} (2 b) - \log_{3} (m)$

Step 4

Multiply the exponents in ${(a^{4})}^{3}$ .

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Step 4.1

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

$\log_{3} (a^{4 \cdot 3}) \log_{3} (2 b) - \log_{3} (m)$

Step 4.2

Multiply $4$ by $3$ .

$\log_{3} (a^{12}) \log_{3} (2 b) - \log_{3} (m)$