Trigonometry Examples

$\log (3) \cdot 15 - \log (3) \cdot 10$

Step 1

Simplify each term.

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Step 1.1

Multiply $\log (3) \cdot 15$ .

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Step 1.1.1

Reorder $\log (3)$ and $15$ .

$15 \cdot \log (3) - \log (3) \cdot 10$

Step 1.1.2

Simplify $15 \cdot \log (3)$ by moving $15$ inside the logarithm.

$\log (3^{15}) - \log (3) \cdot 10$

Step 1.2

Raise $3$ to the power of $15$ .

$\log (14348907) - \log (3) \cdot 10$

Step 1.3

Multiply $- \log (3) \cdot 10$ .

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Step 1.3.1

Multiply $10$ by $- 1$ .

$\log (14348907) - 10 \log (3)$

Step 1.3.2

Simplify $- 10 \log (3)$ by moving $10$ inside the logarithm.

$\log (14348907) - \log (3^{10})$

Step 1.4

Raise $3$ to the power of $10$ .

$\log (14348907) - \log (59049)$

Step 2

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

$\log (\frac{14348907}{59049})$

Step 3

Divide $14348907$ by $59049$ .

$\log (243)$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\log (243)$

Decimal Form:

$2.38560627 \dots$