Precalculus Examples

$\frac{1}{5} \cdot (\log_{3} (x)) + \log_{3} (7) - 2 \log_{4} (y - 3)$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Simplify $\frac{1}{5} (\log_{3} (x))$ by moving $\frac{1}{5}$ inside the logarithm.

$\log_{3} (x^{\frac{1}{5}}) + \log_{3} (7) - 2 \log_{4} (y - 3)$

Step 1.2

Simplify $- 2 \log_{4} (y - 3)$ by moving $2$ inside the logarithm.

$\log_{3} (x^{\frac{1}{5}}) + \log_{3} (7) - \log_{4} ({(y - 3)}^{2})$

Step 2

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

$\log_{3} (x^{\frac{1}{5}} \cdot 7) - \log_{4} ({(y - 3)}^{2})$

Step 3

Move $7$ to the left of $x^{\frac{1}{5}}$ .

$\log_{3} (7 x^{\frac{1}{5}}) - \log_{4} ({(y - 3)}^{2})$