Basic Math Examples

2 {log}_{6} (3) + {log}_{6} (4)

$2 \log_{6} (3) + \log_{6} (4)$

Step 1

Simplify each term.

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Step 1.1

Simplify

2 {log}_{6} (3)

$2 \log_{6} (3)$ by moving

2

$2$ inside the logarithm.

{log}_{6} (3^{2}) + {log}_{6} (4)

$\log_{6} (3^{2}) + \log_{6} (4)$

Step 1.2

Raise

3

$3$ to the power of

2

$2$ .

{log}_{6} (9) + {log}_{6} (4)

$\log_{6} (9) + \log_{6} (4)$

{log}_{6} (9) + {log}_{6} (4)

$\log_{6} (9) + \log_{6} (4)$

Step 2

Use the product property of logarithms,

{log}_{b} (x) + {log}_{b} (y) = {log}_{b} (x y)

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

{log}_{6} (9 \cdot 4)

$\log_{6} (9 \cdot 4)$

Step 3

Multiply

9

$9$ by

4

$4$ .

{log}_{6} (36)

$\log_{6} (36)$

Step 4

Logarithm base

6

$6$ of

36

$36$ is

2

$2$ .

2

$2$

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

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