Precalculus Examples

$\frac{4 (\ln (y))}{\ln (10)} + \frac{2 (\ln (x))}{\ln (10)}$

Step 1

Combine the numerators over the common denominator.

$\frac{4 (\ln (y)) + 2 (\ln (x))}{\ln (10)}$

Step 2

Simplify each term.

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Step 2.1

Simplify $4 (\ln (y))$ by moving $4$ inside the logarithm.

$\frac{\ln (y^{4}) + 2 (\ln (x))}{\ln (10)}$

Step 2.2

Simplify $2 (\ln (x))$ by moving $2$ inside the logarithm.

$\frac{\ln (y^{4}) + \ln (x^{2})}{\ln (10)}$

Step 3

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

$\frac{\ln (y^{4} x^{2})}{\ln (10)}$