Precalculus Examples

$\log (2) \cdot 3 - 2 \log (2) (x + 1)$

Step 1

Simplify each term.

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Step 1.1

Multiply $\log (2) \cdot 3$ .

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Step 1.1.1

Reorder $\log (2)$ and $3$ .

$3 \cdot \log (2) - 2 \log (2) (x + 1)$

Step 1.1.2

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

$\log (2^{3}) - 2 \log (2) (x + 1)$

Step 1.2

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

$\log (8) - 2 \log (2) (x + 1)$

Step 1.3

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

$\log (8) - \log (2^{2}) (x + 1)$

Step 1.4

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

$\log (8) - \log (4) (x + 1)$

Step 1.5

Apply the distributive property.

$\log (8) - \log (4) x - \log (4) \cdot 1$

Step 1.6

Multiply $- 1$ by $1$ .

$\log (8) - \log (4) x - \log (4)$

Step 2

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$- \log (4) x + \log (\frac{8}{4})$

Step 3

Divide $8$ by $4$ .

$- \log (4) x + \log (2)$

Step 4

Reorder factors in $- \log (4) x + \log (2)$ .

$- x \log (4) + \log (2)$