Expand the Logarithmic Expression log base 6 of 36/( square root of x+1)

$\log_{6} (\frac{36}{\sqrt{x + 1}})$

Rewrite $\log_{6} (\frac{36}{\sqrt{x + 1}})$ as $\log_{6} (36) - \log_{6} (\sqrt{x + 1})$ .

$\log_{6} (36) - \log_{6} (\sqrt{x + 1})$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x + 1}$ as ${(x + 1)}^{\frac{1}{2}}$ .

$\log_{6} (36) - \log_{6} ({(x + 1)}^{\frac{1}{2}})$

Expand $\log_{6} ({(x + 1)}^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$\log_{6} (36) - (\frac{1}{2} \log_{6} (x + 1))$

Logarithm base $6$ of $36$ is $2$ .

$2 - (\frac{1}{2} \log_{6} (x + 1))$

Combine $\frac{1}{2}$ and $\log_{6} (x + 1)$ .

$2 - \frac{\log_{6} (x + 1)}{2}$

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$2 \cdot \frac{2}{2} - \frac{\log_{6} (x + 1)}{2}$

Combine $2$ and $\frac{2}{2}$ .

$\frac{2 \cdot 2}{2} - \frac{\log_{6} (x + 1)}{2}$

Combine the numerators over the common denominator.

$\frac{2 \cdot 2 - \log_{6} (x + 1)}{2}$

Multiply $2$ by $2$ .

$\frac{4 - \log_{6} (x + 1)}{2}$