Basic Math Examples

3 {log}_{3} (2) - {log}_{3} (72)

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

Step 1

Simplify each term.

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Step 1.1

Simplify

3 {log}_{3} (2)

$3 \log_{3} (2)$ by moving

3

$3$ inside the logarithm.

{log}_{3} (2^{3}) - {log}_{3} (72)

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

Step 1.2

Raise

2

$2$ to the power of

3

$3$ .

{log}_{3} (8) - {log}_{3} (72)

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

{log}_{3} (8) - {log}_{3} (72)

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

Step 2

Use the quotient property of logarithms,

{log}_{b} (x) - {log}_{b} (y) = {log}_{b} (\frac{x}{y})

$\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

{log}_{3} (\frac{8}{72})

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

Step 3

Cancel the common factor of

8

$8$ and

72

$72$ .

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Step 3.1

Factor

8

$8$ out of

8

$8$ .

{log}_{3} (\frac{8 (1)}{72})

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor

8

$8$ out of

72

$72$ .

{log}_{3} (\frac{8 \cdot 1}{8 \cdot 9})

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

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

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

Step 4

Logarithm base

$3$ of

$\frac{1}{9}$ is

$- 2$ .

$- 2$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$