Algebra Examples

$\log_{(x + 1)} (8) = 3$

Step 1

Rewrite $\log_{x + 1} (8) = 3$ 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 $b^{y} = x$ .

${(x + 1)}^{3} = 8$

Step 2

Solve for $x$ .

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Step 2.1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x + 1 = \sqrt[3]{8}$

Step 2.2

Simplify $\sqrt[3]{8}$ .

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Step 2.2.1

Rewrite $8$ as $2^{3}$ .

$x + 1 = \sqrt[3]{2^{3}}$

Step 2.2.2

Pull terms out from under the radical, assuming real numbers.

$x + 1 = 2$

Step 2.3

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

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Step 2.3.1

Subtract $1$ from both sides of the equation.

$x = 2 - 1$

Step 2.3.2

Subtract $1$ from $2$ .

$x = 1$