Precalculus Examples

$\log_{3} (x^{10} y^{\frac{3}{19}})$

Step 1

Rewrite $\log_{3} (x^{10} y^{\frac{3}{19}})$ as $\log_{3} (x^{10}) + \log_{3} (y^{\frac{3}{19}})$ .

$\log_{3} (x^{10}) + \log_{3} (y^{\frac{3}{19}})$

Step 2

Expand $\log_{3} (x^{10})$ by moving $10$ outside the logarithm.

$10 \log_{3} (x) + \log_{3} (y^{\frac{3}{19}})$

Step 3

Expand $\log_{3} (y^{\frac{3}{19}})$ by moving $\frac{3}{19}$ outside the logarithm.

$10 \log_{3} (x) + \frac{3}{19} \log_{3} (y)$

Step 4

Combine $\frac{3}{19}$ and $\log_{3} (y)$ .

$10 \log_{3} (x) + \frac{3 \log_{3} (y)}{19}$