Precalculus Examples

$\log_{5} (7) + 2 \log_{5} (x) + \log_{5} (y)$

Step 1

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

$2 \log_{5} (x) + \log_{5} (7 y)$

Step 2

Simplify $2 \log_{5} (x)$ by moving $2$ inside the logarithm.

$\log_{5} (x^{2}) + \log_{5} (7 y)$

Step 3

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

$\log_{5} (x^{2} (7 y))$

Step 4

Rewrite using the commutative property of multiplication.

$\log_{5} (7 x^{2} y)$