Finite Math Examples

$4 + \log_{3} (x + 9) = 8$

Step 1

Move all terms not containing $\log_{3} (x + 9)$ to the right side of the equation.

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Step 1.1

Subtract $4$ from both sides of the equation.

$\log_{3} (x + 9) = 8 - 4$

Step 1.2

Subtract $4$ from $8$ .

$\log_{3} (x + 9) = 4$

Step 2

Rewrite $\log_{3} (x + 9) = 4$ 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 $b^{y} = x$ .

$3^{4} = x + 9$

Step 3

Solve for $x$ .

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Step 3.1

Rewrite the equation as $x + 9 = 3^{4}$ .

$x + 9 = 3^{4}$

Step 3.2

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

$x + 9 = 81$

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 $9$ from both sides of the equation.

$x = 81 - 9$

Step 3.3.2

Subtract $9$ from $81$ .

$x = 72$