Basic Math Examples

$3 \log_{3} (2) - \log_{3} (72)$

Step 1

Simplify each term.

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Step 1.1

Simplify $3 \log_{3} (2)$ by moving $3$ inside the logarithm.

$\log_{3} (2^{3}) - \log_{3} (72)$

Step 1.2

Raise $2$ to the power of $3$ .

$\log_{3} (8) - \log_{3} (72)$

Step 2

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

$\log_{3} (\frac{8}{72})$

Step 3

Cancel the common factor of $8$ and $72$ .

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Step 3.1

Factor $8$ out of $8$ .

$\log_{3} (\frac{8 (1)}{72})$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $8$ out of $72$ .

$\log_{3} (\frac{8 \cdot 1}{8 \cdot 9})$

Step 3.2.2

Cancel the common factor.

$\log_{3} (\frac{8 \cdot 1}{8 \cdot 9})$

Step 3.2.3

Rewrite the expression.

$\log_{3} (\frac{1}{9})$

Step 4

Logarithm base $3$ of $\frac{1}{9}$ is $- 2$ .

$- 2$