Precalculus Examples

$2 = \log (3 x + 4)$

Step 1

Rewrite the equation as $\log (3 x + 4) = 2$ .

$\log (3 x + 4) = 2$

Step 2

Rewrite $\log (3 x + 4) = 2$ 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 $b^{y} = x$ .

$10^{2} = 3 x + 4$

Step 3

Solve for $x$ .

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Step 3.1

Rewrite the equation as $3 x + 4 = 10^{2}$ .

$3 x + 4 = 10^{2}$

Step 3.2

Raise $10$ to the power of $2$ .

$3 x + 4 = 100$

Step 3.3

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

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Step 3.3.1

Subtract $4$ from both sides of the equation.

$3 x = 100 - 4$

Step 3.3.2

Subtract $4$ from $100$ .

$3 x = 96$

Step 3.4

Divide each term in $3 x = 96$ by $3$ and simplify.

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Step 3.4.1

Divide each term in $3 x = 96$ by $3$ .

$\frac{3 x}{3} = \frac{96}{3}$

Step 3.4.2

Simplify the left side.

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Step 3.4.2.1

Cancel the common factor of $3$ .

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Step 3.4.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{96}{3}$

Step 3.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{96}{3}$

Step 3.4.3

Simplify the right side.

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Step 3.4.3.1

Divide $96$ by $3$ .

$x = 32$