Finite Math Examples

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

Step 1

Subtract $6$ from both sides of the equation.

$\log_{6} (2 x - 6) - 6 = 0$

Step 2

Add $6$ to both sides of the equation.

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

Step 3

Rewrite $\log_{6} (2 x - 6) = 6$ 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 $b^{y} = x$ .

$6^{6} = 2 x - 6$

Step 4

Solve for $x$ .

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Step 4.1

Rewrite the equation as $2 x - 6 = 6^{6}$ .

$2 x - 6 = 6^{6}$

Step 4.2

Raise $6$ to the power of $6$ .

$2 x - 6 = 46656$

Step 4.3

Move all terms not containing $x$ to the right side of the equation.

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Step 4.3.1

Add $6$ to both sides of the equation.

$2 x = 46656 + 6$

Step 4.3.2

Add $46656$ and $6$ .

$2 x = 46662$

Step 4.4

Divide each term in $2 x = 46662$ by $2$ and simplify.

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Step 4.4.1

Divide each term in $2 x = 46662$ by $2$ .

$\frac{2 x}{2} = \frac{46662}{2}$

Step 4.4.2

Simplify the left side.

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Step 4.4.2.1

Cancel the common factor of $2$ .

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Step 4.4.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{46662}{2}$

Step 4.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{46662}{2}$

Step 4.4.3

Simplify the right side.

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Step 4.4.3.1

Divide $46662$ by $2$ .

$x = 23331$