Algebra Examples

$\log_{9} (6 x^{3} y^{5} z)$

Step 1

Rewrite $\log_{9} (6 x^{3} y^{5} z)$ as $\log_{9} (6 x^{3} y^{5}) + \log_{9} (z)$ .

$\log_{9} (6 x^{3} y^{5}) + \log_{9} (z)$

Step 2

Rewrite $\log_{9} (6 x^{3} y^{5})$ as $\log_{9} (6 x^{3}) + \log_{9} (y^{5})$ .

$\log_{9} (6 x^{3}) + \log_{9} (y^{5}) + \log_{9} (z)$

Step 3

Rewrite $\log_{9} (6 x^{3})$ as $\log_{9} (6) + \log_{9} (x^{3})$ .

$\log_{9} (6) + \log_{9} (x^{3}) + \log_{9} (y^{5}) + \log_{9} (z)$

Step 4

Expand $\log_{9} (x^{3})$ by moving $3$ outside the logarithm.

$\log_{9} (6) + 3 \log_{9} (x) + \log_{9} (y^{5}) + \log_{9} (z)$

Step 5

Expand $\log_{9} (y^{5})$ by moving $5$ outside the logarithm.

$\log_{9} (6) + 3 \log_{9} (x) + 5 \log_{9} (y) + \log_{9} (z)$

Step 6

Simplify each term.

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Step 6.1

Rewrite $\log_{9} (6)$ as $\log_{9} (2 (3))$ .

$\log_{9} (2 (3)) + 3 \log_{9} (x) + 5 \log_{9} (y) + \log_{9} (z)$

Step 6.2

Rewrite $\log_{9} (2 (3))$ as $\log_{9} (2) + \log_{9} (3)$ .

$\log_{9} (2) + \log_{9} (3) + 3 \log_{9} (x) + 5 \log_{9} (y) + \log_{9} (z)$

Step 6.3

Logarithm base $9$ of $3$ is $\frac{1}{2}$ .

$\log_{9} (2) + \frac{1}{2} + 3 \log_{9} (x) + 5 \log_{9} (y) + \log_{9} (z)$