Precalculus Examples

$\log_{4} (7 x - 6) = 3$

Step 1

Rewrite $\log_{4} (7 x - 6) = 3$ 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 $b^{y} = x$ .

$4^{3} = 7 x - 6$

Step 2

Solve for $x$ .

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Step 2.1

Rewrite the equation as $7 x - 6 = 4^{3}$ .

$7 x - 6 = 4^{3}$

Step 2.2

Raise $4$ to the power of $3$ .

$7 x - 6 = 64$

Step 2.3

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

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Step 2.3.1

Add $6$ to both sides of the equation.

$7 x = 64 + 6$

Step 2.3.2

Add $64$ and $6$ .

$7 x = 70$

Step 2.4

Divide each term in $7 x = 70$ by $7$ and simplify.

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Step 2.4.1

Divide each term in $7 x = 70$ by $7$ .

$\frac{7 x}{7} = \frac{70}{7}$

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Cancel the common factor of $7$ .

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Step 2.4.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{70}{7}$

Step 2.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{70}{7}$

Step 2.4.3

Simplify the right side.

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Step 2.4.3.1

Divide $70$ by $7$ .

$x = 10$