Precalculus Examples

$3 \log ({(3)}^{5}) - \log ({(3)}^{4})$

Step 1

Simplify each term.

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Step 1.1

Raise $3$ to the power of $5$ .

$3 \log (243) - \log ({(3)}^{4})$

Step 1.2

Simplify $3 \log (243)$ by moving $3$ inside the logarithm.

$\log (243^{3}) - \log ({(3)}^{4})$

Step 1.3

Raise $243$ to the power of $3$ .

$\log (14348907) - \log ({(3)}^{4})$

Step 1.4

Raise $3$ to the power of $4$ .

$\log (14348907) - \log (81)$

Step 2

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log (\frac{14348907}{81})$

Step 3

Divide $14348907$ by $81$ .

$\log (177147)$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\log (177147)$

Decimal Form:

$5.24833380 \dots$