Algebra Examples

$\log_{3} (\frac{x^{3}}{7 y^{\frac{3}{2}}})$

Step 1

Rewrite $\log_{3} (\frac{x^{3}}{7 y^{\frac{3}{2}}})$ as $\log_{3} (x^{3}) - \log_{3} (7 y^{\frac{3}{2}})$ .

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

Step 2

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

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

Step 3

Rewrite $\log_{3} (7 y^{\frac{3}{2}})$ as $\log_{3} (7) + \log_{3} (y^{\frac{3}{2}})$ .

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

Step 4

Expand $\log_{3} (y^{\frac{3}{2}})$ by moving $\frac{3}{2}$ outside the logarithm.

$3 \log_{3} (x) - (\log_{3} (7) + \frac{3}{2} \log_{3} (y))$

Step 5

Simplify each term.

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Step 5.1

Combine $\frac{3}{2}$ and $\log_{3} (y)$ .

$3 \log_{3} (x) - (\log_{3} (7) + \frac{3 \log_{3} (y)}{2})$

Step 5.2

Apply the distributive property.

$3 \log_{3} (x) - \log_{3} (7) - \frac{3 \log_{3} (y)}{2}$