Algebra Examples

$\log_{b} (\frac{4^{2} x^{3}}{y})$

Step 1

Rewrite $\log_{b} (\frac{4^{2} x^{3}}{y})$ as $\log_{b} (4^{2} x^{3}) - \log_{b} (y)$ .

$\log_{b} (4^{2} x^{3}) - \log_{b} (y)$

Step 2

Rewrite $\log_{b} (4^{2} x^{3})$ as $\log_{b} (4^{2}) + \log_{b} (x^{3})$ .

$\log_{b} (4^{2}) + \log_{b} (x^{3}) - \log_{b} (y)$

Step 3

Expand $\log_{b} (4^{2})$ by moving $2$ outside the logarithm.

$2 \log_{b} (4) + \log_{b} (x^{3}) - \log_{b} (y)$

Step 4

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

$2 \log_{b} (4) + 3 \log_{b} (x) - \log_{b} (y)$

Step 5

Simplify each term.

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Step 5.1

Rewrite $\log_{b} (4)$ as $\log_{b} (2^{2})$ .

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

Step 5.2

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

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

Step 5.3

Multiply $2$ by $2$ .

$4 \log_{b} (2) + 3 \log_{b} (x) - \log_{b} (y)$