Precalculus Examples

$3 \log (2) + 4 \log (x) - 2 \log (4)$

Step 1

Simplify each term.

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Step 1.1

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

$\log (2^{3}) + 4 \log (x) - 2 \log (4)$

Step 1.2

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

$\log (8) + 4 \log (x) - 2 \log (4)$

Step 1.3

Simplify $4 \log (x)$ by moving $4$ inside the logarithm.

$\log (8) + \log (x^{4}) - 2 \log (4)$

Step 1.4

Simplify $- 2 \log (4)$ by moving $2$ inside the logarithm.

$\log (8) + \log (x^{4}) - \log (4^{2})$

Step 1.5

Raise $4$ to the power of $2$ .

$\log (8) + \log (x^{4}) - \log (16)$

Step 2

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log (8 x^{4}) - \log (16)$

Step 3

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

$\log (\frac{8 x^{4}}{16})$

Step 4

Cancel the common factor of $8$ and $16$ .

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Step 4.1

Factor $8$ out of $8 x^{4}$ .

$\log (\frac{8 (x^{4})}{16})$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $8$ out of $16$ .

$\log (\frac{8 x^{4}}{8 \cdot 2})$

Step 4.2.2

Cancel the common factor.

$\log (\frac{8 x^{4}}{8 \cdot 2})$

Step 4.2.3

Rewrite the expression.

$\log (\frac{x^{4}}{2})$