Algebra Examples

\ln ({(\frac{3 x}{y^{2}})}^{4})

$\ln ({(\frac{3 x}{y^{2}})}^{4})$

Step 1

Expand

\ln ({(\frac{3 x}{y^{2}})}^{4})

$\ln ({(\frac{3 x}{y^{2}})}^{4})$ by moving

4

$4$ outside the logarithm.

4 \ln (\frac{3 x}{y^{2}})

$4 \ln (\frac{3 x}{y^{2}})$

Step 2

Rewrite

\ln (\frac{3 x}{y^{2}})

$\ln (\frac{3 x}{y^{2}})$ as

\ln (3 x) - \ln (y^{2})

$\ln (3 x) - \ln (y^{2})$ .

4 (\ln (3 x) - \ln (y^{2}))

$4 (\ln (3 x) - \ln (y^{2}))$

Step 3

Expand

\ln (y^{2})

$\ln (y^{2})$ by moving

2

$2$ outside the logarithm.

4 (\ln (3 x) - (2 \ln (y)))

$4 (\ln (3 x) - (2 \ln (y)))$

Step 4

Multiply

2

$2$ by

- 1

$- 1$ .

4 (\ln (3 x) - 2 \ln (y))

$4 (\ln (3 x) - 2 \ln (y))$

Step 5

Rewrite

\ln (3 x)

$\ln (3 x)$ as

\ln (3) + \ln (x)

$\ln (3) + \ln (x)$ .

4 (\ln (3) + \ln (x) - 2 \ln (y))

$4 (\ln (3) + \ln (x) - 2 \ln (y))$

Step 6

Apply the distributive property.

4 \ln (3) + 4 \ln (x) + 4 (- 2 \ln (y))

$4 \ln (3) + 4 \ln (x) + 4 (- 2 \ln (y))$

Step 7

Multiply

- 2

$- 2$ by

4

$4$ .

4 \ln (3) + 4 \ln (x) - 8 \ln (y)

$4 \ln (3) + 4 \ln (x) - 8 \ln (y)$

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

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