Precalculus Examples

$\log (\frac{x^{7} y^{2}}{z^{4} t^{5}})$

Rewrite $\log (\frac{x^{7} y^{2}}{z^{4} t^{5}})$ as $\log (x^{7} y^{2}) - \log (z^{4} t^{5})$ .

$\log (x^{7} y^{2}) - \log (z^{4} t^{5})$

Rewrite $\log (x^{7} y^{2})$ as $\log (x^{7}) + \log (y^{2})$ .

$\log (x^{7}) + \log (y^{2}) - \log (z^{4} t^{5})$

Expand $\log (x^{7})$ by moving $7$ outside the logarithm.

$7 \log (x) + \log (y^{2}) - \log (z^{4} t^{5})$

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

$7 \log (x) + 2 \log (y) - \log (z^{4} t^{5})$

Rewrite $\log (z^{4} t^{5})$ as $\log (z^{4}) + \log (t^{5})$ .

$7 \log (x) + 2 \log (y) - (\log (z^{4}) + \log (t^{5}))$

Expand $\log (z^{4})$ by moving $4$ outside the logarithm.

$7 \log (x) + 2 \log (y) - (4 \log (z) + \log (t^{5}))$

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

$7 \log (x) + 2 \log (y) - (4 \log (z) + 5 \log (t))$

Simplify each term.

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Apply the distributive property.

$7 \log (x) + 2 \log (y) - (4 \log (z)) - (5 \log (t))$

Multiply $4$ by $- 1$ .

$7 \log (x) + 2 \log (y) - 4 \log (z) - (5 \log (t))$

Multiply $5$ by $- 1$ .

$7 \log (x) + 2 \log (y) - 4 \log (z) - 5 \log (t)$