Solve for x 2 log base 6 of x=2

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

Step 1

Divide each term in $2 \log_{6} (x) = 2$ by $2$ and simplify.

Divide each term in $2 \log_{6} (x) = 2$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $\log_{6} (x)$ by $1$ .

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

Simplify the right side.

Divide $2$ by $2$ .

$\log_{6} (x) = 1$

Step 2

Rewrite $\log_{6} (x) = 1$ 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 $b^{y} = x$ .

$6^{1} = x$

Step 3

Rewrite the equation as $x = 6^{1}$ .

$x = 6$

Solve for x 2 log base 6 of x=2

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