Solve for x 3 log base 2 of x+4=13

$3 \log_{2} (x + 4) = 13$

Divide each term in $3 \log_{2} (x + 4) = 13$ by $3$ and simplify.

Divide each term in $3 \log_{2} (x + 4) = 13$ by $3$ .

$\frac{3 \log_{2} (x + 4)}{3} = \frac{13}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 \log_{2} (x + 4)}{3} = \frac{13}{3}$

Divide $\log_{2} (x + 4)$ by $1$ .

$\log_{2} (x + 4) = \frac{13}{3}$

Rewrite $\log_{2} (x + 4) = \frac{13}{3}$ 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 $b^{y} = x$ .

$2^{\frac{13}{3}} = x + 4$

Solve for $x$ .

Rewrite the equation as $x + 4 = 2^{\frac{13}{3}}$ .

$x + 4 = 2^{\frac{13}{3}}$

Subtract $4$ from both sides of the equation.

$x = 2^{\frac{13}{3}} - 4$

The result can be shown in multiple forms.

Exact Form:

$x = 2^{\frac{13}{3}} - 4$

Decimal Form:

$x = 16.15873679 \dots$

Solve for x 3 log base 2 of x+4=13

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