Precalculus Examples

$\log_{5} (4) + 3 \log_{5} (x) - \log_{5} (7 y)$

Step 1

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

$3 \log_{5} (x) + \log_{5} (\frac{4}{7 y})$

Step 2

Simplify $3 \log_{5} (x)$ by moving $3$ inside the logarithm.

$\log_{5} (x^{3}) + \log_{5} (\frac{4}{7 y})$

Step 3

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

$\log_{5} (x^{3} \frac{4}{7 y})$

Step 4

Combine $x^{3}$ and $\frac{4}{7 y}$ .

$\log_{5} (\frac{x^{3} \cdot 4}{7 y})$

Step 5

Move $4$ to the left of $x^{3}$ .

$\log_{5} (\frac{4 x^{3}}{7 y})$