Precalculus Examples

$7 \log (3) a + \log (3) b - 2 \log (3) (8 c)$

Step 1

Simplify each term.

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Step 1.1

Simplify $7 \log (3)$ by moving $7$ inside the logarithm.

$\log (3^{7}) a + \log (3) b - 2 \log (3) (8 c)$

Step 1.2

Raise $3$ to the power of $7$ .

$\log (2187) a + \log (3) b - 2 \log (3) (8 c)$

Step 1.3

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

$\log (2187) a + \log (3) b - \log (3^{2}) (8 c)$

Step 1.4

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

$\log (2187) a + \log (3) b - \log (9) (8 c)$

Step 1.5

Multiply $- \log (9) (8 c)$ .

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Step 1.5.1

Multiply $8$ by $- 1$ .

$\log (2187) a + \log (3) b - 8 \log (9) c$

Step 1.5.2

Simplify $- 8 \log (9)$ by moving $8$ inside the logarithm.

$\log (2187) a + \log (3) b - \log (9^{8}) c$

Step 1.6

Raise $9$ to the power of $8$ .

$\log (2187) a + \log (3) b - \log (43046721) c$

Step 2

Reorder factors in $\log (2187) a + \log (3) b - \log (43046721) c$ .

$a \log (2187) + b \log (3) - c \log (43046721)$