Precalculus Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

$\log (16) - (\log (3)) + 2 \log (x - 4)$

Step 1.3

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

$\log (16) - \log (3) + \log ({(x - 4)}^{2})$

Step 2

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

$\log (\frac{16}{3}) + \log ({(x - 4)}^{2})$

Step 3

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

$\log (\frac{16}{3} {(x - 4)}^{2})$

Step 4

Combine $\frac{16}{3}$ and ${(x - 4)}^{2}$ .

$\log (\frac{16 {(x - 4)}^{2}}{3})$