Precalculus Examples

$2 (\log (2 x - \log (y))) - (\log (3) + 2 \log (5))$

Step 1

Simplify each term.

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Step 1.1

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

$\log ({(2 x - \log (y))}^{2}) - (\log (3) + 2 \log (5))$

Step 1.2

Simplify each term.

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Step 1.2.1

Simplify $2 \log (5)$ by moving $2$ inside the logarithm.

$\log ({(2 x - \log (y))}^{2}) - (\log (3) + \log (5^{2}))$

Step 1.2.2

Raise $5$ to the power of $2$ .

$\log ({(2 x - \log (y))}^{2}) - (\log (3) + \log (25))$

Step 1.3

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

$\log ({(2 x - \log (y))}^{2}) - \log (3 \cdot 25)$

Step 1.4

Multiply $3$ by $25$ .

$\log ({(2 x - \log (y))}^{2}) - \log (75)$

Step 2

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

$\log (\frac{{(2 x - \log (y))}^{2}}{75})$