Algebra Examples

$\frac{1}{3} \log_{2} (x) + 5 = 7$

Step 1

Combine $\frac{1}{3}$ and $\log_{2} (x)$ .

$\frac{\log_{2} (x)}{3} + 5 = 7$

Step 2

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

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Step 2.1

Subtract $5$ from both sides of the equation.

$\frac{\log_{2} (x)}{3} = 7 - 5$

Step 2.2

Subtract $5$ from $7$ .

$\frac{\log_{2} (x)}{3} = 2$

Step 3

Multiply both sides of the equation by $3$ .

$3 \frac{\log_{2} (x)}{3} = 3 \cdot 2$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1

Cancel the common factor.

$3 \frac{\log_{2} (x)}{3} = 3 \cdot 2$

Step 4.1.1.2

Rewrite the expression.

$\log_{2} (x) = 3 \cdot 2$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $3$ by $2$ .

$\log_{2} (x) = 6$

Step 5

Rewrite $\log_{2} (x) = 6$ 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 $b^{y} = x$ .

$2^{6} = x$

Step 6

Solve for $x$ .

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Step 6.1

Rewrite the equation as $x = 2^{6}$ .

$x = 2^{6}$

Step 6.2

Raise $2$ to the power of $6$ .

$x = 64$