Precalculus Examples

$3 \log (6) x + 5 \log (6) (x - 6)$

Step 1

Simplify each term.

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Step 1.1

Simplify $3 \log (6)$ by moving $3$ inside the logarithm.

$\log (6^{3}) x + 5 \log (6) (x - 6)$

Step 1.2

Raise $6$ to the power of $3$ .

$\log (216) x + 5 \log (6) (x - 6)$

Step 1.3

Simplify $5 \log (6)$ by moving $5$ inside the logarithm.

$\log (216) x + \log (6^{5}) (x - 6)$

Step 1.4

Raise $6$ to the power of $5$ .

$\log (216) x + \log (7776) (x - 6)$

Step 1.5

Apply the distributive property.

$\log (216) x + \log (7776) x + \log (7776) \cdot - 6$

Step 1.6

Multiply $\log (7776) \cdot - 6$ .

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Step 1.6.1

Reorder $\log (7776)$ and $- 6$ .

$\log (216) x + \log (7776) x - 6 \cdot \log (7776)$

Step 1.6.2

Simplify $- 6 \cdot \log (7776)$ by moving $6$ inside the logarithm.

$\log (216) x + \log (7776) x - \log (7776^{6})$

Step 1.7

Raise $7776$ to the power of $6$ .

$\log (216) x + \log (7776) x - \log (221073919720733000000000)$

Step 2

Reorder factors in $\log (216) x + \log (7776) x - \log (221073919720733000000000)$ .

$x \log (216) + x \log (7776) - \log (221073919720733000000000)$