Solve for x 3 log base 2 of 2x=3

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

Divide each term by $3$ and simplify.

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

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

Cancel the common factor of $3$ .

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Cancel the common factor.

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

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

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

Divide $3$ by $3$ .

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

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 $b^{y} = x$ .

$2^{1} = 2 x$

Solve for $x$

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Evaluate the exponent.

$2 = 2 x$

Rewrite the equation as $2 x = 2$ .

$2 x = 2$

Divide each term by $2$ and simplify.

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Divide each term in $2 x = 2$ by $2$ .

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

Cancel the common factor of $2$ .

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Cancel the common factor.

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

Divide $x$ by $1$ .

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

Divide $2$ by $2$ .

$x = 1$

Solve for x 3 log base 2 of 2x=3

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