Solve for x 4+4* log base 2 of x=14

$4 + 4 \cdot \log_{2} (x) = 14$

Step 1

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

Subtract $4$ from both sides of the equation.

$4 \log_{2} (x) = 14 - 4$

Subtract $4$ from $14$ .

$4 \log_{2} (x) = 10$

Step 2

Divide each term in $4 \log_{2} (x) = 10$ by $4$ and simplify.

Divide each term in $4 \log_{2} (x) = 10$ by $4$ .

$\frac{4 \log_{2} (x)}{4} = \frac{10}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 \log_{2} (x)}{4} = \frac{10}{4}$

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

$\log_{2} (x) = \frac{10}{4}$

Simplify the right side.

Cancel the common factor of $10$ and $4$ .

Factor $2$ out of $10$ .

$\log_{2} (x) = \frac{2 (5)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

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

$2^{\frac{5}{2}} = x$

Step 4

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

$x = 2^{\frac{5}{2}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = 2^{\frac{5}{2}}$

Decimal Form:

$x = 5.65685424 \dots$

Solve for x 4+4* log base 2 of x=14

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