Algebra Examples

$\log_{3} (4 + \log_{2} (x)) = 2$

Step 1

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

$3^{2} = 4 + \log_{2} (x)$

Step 2

Solve for $x$ .

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Step 2.1

Rewrite the equation as $4 + \log_{2} (x) = 3^{2}$ .

$4 + \log_{2} (x) = 3^{2}$

Step 2.2

Raise $3$ to the power of $2$ .

$4 + \log_{2} (x) = 9$

Step 2.3

Move all terms not containing $\log_{2} (x)$ to the right side of the equation.

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Step 2.3.1

Subtract $4$ from both sides of the equation.

$\log_{2} (x) = 9 - 4$

Step 2.3.2

Subtract $4$ from $9$ .

$\log_{2} (x) = 5$

Step 2.4

Rewrite $\log_{2} (x) = 5$ 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 $b^{y} = x$ .

$2^{5} = x$

Step 2.5

Solve for $x$ .

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Step 2.5.1

Rewrite the equation as $x = 2^{5}$ .

$x = 2^{5}$

Step 2.5.2

Raise $2$ to the power of $5$ .

$x = 32$