Precalculus Examples

$18 - \log_{2} (x - 4) = 7$

Step 1

Move all terms not containing $\log_{2} (x - 4)$ to the right side of the equation.

Tap for more steps...

Step 1.1

Subtract $18$ from both sides of the equation.

$- \log_{2} (x - 4) = 7 - 18$

Step 1.2

Subtract $18$ from $7$ .

$- \log_{2} (x - 4) = - 11$

Step 2

Divide each term in $- \log_{2} (x - 4) = - 11$ by $- 1$ and simplify.

Tap for more steps...

Step 2.1

Divide each term in $- \log_{2} (x - 4) = - 11$ by $- 1$ .

$\frac{- \log_{2} (x - 4)}{- 1} = \frac{- 11}{- 1}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Dividing two negative values results in a positive value.

$\frac{\log_{2} (x - 4)}{1} = \frac{- 11}{- 1}$

Step 2.2.2

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

$\log_{2} (x - 4) = \frac{- 11}{- 1}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Divide $- 11$ by $- 1$ .

$\log_{2} (x - 4) = 11$

Step 3

Rewrite $\log_{2} (x - 4) = 11$ 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 $b^{y} = x$ .

$2^{11} = x - 4$

Step 4

Solve for $x$ .

Tap for more steps...

Step 4.1

Rewrite the equation as $x - 4 = 2^{11}$ .

$x - 4 = 2^{11}$

Step 4.2

Raise $2$ to the power of $11$ .

$x - 4 = 2048$

Step 4.3

Move all terms not containing $x$ to the right side of the equation.

Tap for more steps...

Step 4.3.1

Add $4$ to both sides of the equation.

$x = 2048 + 4$

Step 4.3.2

Add $2048$ and $4$ .

$x = 2052$