Solve for x log base 5 of 2x=1/6

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

Step 1

Rewrite $\log_{5} (2 x) = \frac{1}{6}$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

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

Step 2

Solve for $x$ .

Rewrite the equation as $2 x = 5^{\frac{1}{6}}$ .

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

Divide each term in $2 x = 5^{\frac{1}{6}}$ by $2$ and simplify.

Divide each term in $2 x = 5^{\frac{1}{6}}$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.65383024 \dots$

Solve for x log base 5 of 2x=1/6

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