Algebra Examples

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

Step 1

Divide each term in $3 \log_{2} (2 x) = 3$ by $3$ and simplify.

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Step 1.1

Divide each term in $3 \log_{2} (2 x) = 3$ by $3$ .

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

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $3$ .

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Step 1.2.1.1

Cancel the common factor.

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

Step 1.2.1.2

Divide $\log_{2} (2 x)$ by $1$ .

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

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $3$ by $3$ .

$\log_{2} (2 x) = 1$

Step 2

Rewrite $\log_{2} (2 x) = 1$ 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 $b^{y} = x$ .

$2^{1} = 2 x$

Step 3

Solve for $x$ .

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Step 3.1

Rewrite the equation as $2 x = 2^{1}$ .

$2 x = 2$

Step 3.2

Divide each term in $2 x = 2^{1}$ by $2$ and simplify.

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Step 3.2.1

Divide each term in $2 x = 2^{1}$ by $2$ .

$\frac{2 x}{2} = \frac{2^{1}}{2}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $2$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{2^{1}}{2}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{2^{1}}{2}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Cancel the common factor of $2^{1}$ and $2$ .

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Step 3.2.3.1.1

Factor $2$ out of $2^{1}$ .

$x = \frac{2 \cdot 1}{2}$

Step 3.2.3.1.2

Cancel the common factors.

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Step 3.2.3.1.2.1

Factor $2$ out of $2$ .

$x = \frac{2 \cdot 1}{2 (1)}$

Step 3.2.3.1.2.2

Cancel the common factor.

$x = \frac{2 \cdot 1}{2 \cdot 1}$

Step 3.2.3.1.2.3

Rewrite the expression.

$x = \frac{1}{1}$

Step 3.2.3.1.2.4

Rewrite the expression.

$x = 1$