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Algebra Examples

{log}_{3} (4 x^{3})

$\log_{3} (4 x^{3})$

Step 1

Rewrite

{log}_{3} (4 x^{3})

$\log_{3} (4 x^{3})$ as

{log}_{3} (4) + {log}_{3} (x^{3})

$\log_{3} (4) + \log_{3} (x^{3})$ .

{log}_{3} (4) + {log}_{3} (x^{3})

$\log_{3} (4) + \log_{3} (x^{3})$

Step 2

Expand

{log}_{3} (x^{3})

$\log_{3} (x^{3})$ by moving

3

$3$ outside the logarithm.

{log}_{3} (4) + 3 {log}_{3} (x)

$\log_{3} (4) + 3 \log_{3} (x)$

Step 3

Simplify each term.

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Step 3.1

Rewrite

{log}_{3} (4)

$\log_{3} (4)$ as

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

$\log_{3} (2^{2})$ .

{log}_{3} (2^{2}) + 3 {log}_{3} (x)

$\log_{3} (2^{2}) + 3 \log_{3} (x)$

Step 3.2

Expand

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

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

2

$2$ outside the logarithm.

2 {log}_{3} (2) + 3 {log}_{3} (x)

$2 \log_{3} (2) + 3 \log_{3} (x)$

2 {log}_{3} (2) + 3 {log}_{3} (x)

$2 \log_{3} (2) + 3 \log_{3} (x)$

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⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

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