Algebra Examples

$3 x = \log_{6} (216)$

Step 1

Divide each term in $3 x = \log_{6} (216)$ by $3$ .

$\frac{3 x}{3} = \frac{\log_{6} (216)}{3}$

Step 2

Simplify the left side.

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Step 2.1

Cancel the common factor of $3$ .

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Step 2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{\log_{6} (216)}{3}$

Step 2.1.2

Divide $x$ by $1$ .

$x = \frac{\log_{6} (216)}{3}$

Step 3

Simplify the right side.

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Step 3.1

Rewrite $\frac{\log_{6} (216)}{3}$ as $\frac{1}{3} \log_{6} (216)$ .

$x = \frac{1}{3} \log_{6} (216)$

Step 3.2

Simplify $\frac{1}{3} \log_{6} (216)$ by moving $\frac{1}{3}$ inside the logarithm.

$x = \log_{6} (216^{\frac{1}{3}})$

Step 3.3

Simplify the expression.

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Step 3.3.1

Rewrite $216$ as $6^{3}$ .

$x = \log_{6} ({(6^{3})}^{\frac{1}{3}})$

Step 3.3.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x = \log_{6} (6^{3 (\frac{1}{3})})$

Step 3.4

Cancel the common factor of $3$ .

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Step 3.4.1

Cancel the common factor.

$x = \log_{6} (6^{3 (\frac{1}{3})})$

Step 3.4.2

Rewrite the expression.

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

Step 3.5

Evaluate the exponent.

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

Step 3.6

Logarithm base $6$ of $6$ is $1$ .

$x = 1$