Finite Math Examples

$\log (8 x^{5} y)$

Step 1

Rewrite $\log (8 x^{5} y)$ as $\log (8 x^{5}) + \log (y)$ .

$\log (8 x^{5}) + \log (y)$

Step 2

Rewrite $\log (8 x^{5})$ as $\log (8) + \log (x^{5})$ .

$\log (8) + \log (x^{5}) + \log (y)$

Step 3

Expand $\log (x^{5})$ by moving $5$ outside the logarithm.

$\log (8) + 5 \log (x) + \log (y)$

Step 4

Simplify each term.

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Step 4.1

Rewrite $\log (8)$ as $\log (2^{3})$ .

$\log (2^{3}) + 5 \log (x) + \log (y)$

Step 4.2

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

$3 \log (2) + 5 \log (x) + \log (y)$