Precalculus Examples

$4 \log (x - 6) = 11$

Step 1

Divide each term in $4 \log (x - 6) = 11$ by $4$ and simplify.

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Step 1.1

Divide each term in $4 \log (x - 6) = 11$ by $4$ .

$\frac{4 \log (x - 6)}{4} = \frac{11}{4}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $4$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{4 \log (x - 6)}{4} = \frac{11}{4}$

Step 1.2.1.2

Divide $\log (x - 6)$ by $1$ .

$\log (x - 6) = \frac{11}{4}$

Step 2

Rewrite $\log (x - 6) = \frac{11}{4}$ 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 $b^{y} = x$ .

$10^{\frac{11}{4}} = x - 6$

Step 3

Solve for $x$ .

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Step 3.1

Rewrite the equation as $x - 6 = 10^{\frac{11}{4}}$ .

$x - 6 = 10^{\frac{11}{4}}$

Step 3.2

Add $6$ to both sides of the equation.

$x = 10^{\frac{11}{4}} + 6$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = 10^{\frac{11}{4}} + 6$

Decimal Form:

$x = 568.34132519 \dots$