Trigonometry Examples

$\frac{\log_{6} (5 x)}{5} = \frac{2}{5}$

Step 1

Simplify $\frac{\log_{6} (5 x)}{5}$ .

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Step 1.1

Rewrite $\frac{\log_{6} (5 x)}{5}$ as $\frac{1}{5} \log_{6} (5 x)$ .

$\frac{1}{5} \log_{6} (5 x) = \frac{2}{5}$

Step 1.2

Simplify $\frac{1}{5} \log_{6} (5 x)$ by moving $\frac{1}{5}$ inside the logarithm.

$\log_{6} ({(5 x)}^{\frac{1}{5}}) = \frac{2}{5}$

Step 1.3

Apply the product rule to $5 x$ .

$\log_{6} (5^{\frac{1}{5}} x^{\frac{1}{5}}) = \frac{2}{5}$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = \frac{36}{5}$

Step 3