Solve by Factoring 11-4^x=5

$11 - 4^{x} = 5$

Step 1

Subtract $5$ from both sides of the equation.

$11 - 4^{x} - 5 = 0$

Step 2

Subtract $5$ from $11$ .

$6 - 4^{x} = 0$

Step 3

Subtract $6$ from both sides of the equation.

$- 4^{x} = - 6$

Step 4

Divide each term in $- 4^{x} = - 6$ by $- 1$ and simplify.

Divide each term in $- 4^{x} = - 6$ by $- 1$ .

$\frac{- 4^{x}}{- 1} = \frac{- 6}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{4^{x}}{1} = \frac{- 6}{- 1}$

Divide $4^{x}$ by $1$ .

$4^{x} = \frac{- 6}{- 1}$

Simplify the right side.

Divide $- 6$ by $- 1$ .

$4^{x} = 6$

Step 5

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (4^{x}) = \ln (6)$

Step 6

Expand $\ln (4^{x})$ by moving $x$ outside the logarithm.

$x \ln (4) = \ln (6)$

Step 7

Divide each term in $x \ln (4) = \ln (6)$ by $\ln (4)$ and simplify.

Divide each term in $x \ln (4) = \ln (6)$ by $\ln (4)$ .

$\frac{x \ln (4)}{\ln (4)} = \frac{\ln (6)}{\ln (4)}$

Simplify the left side.

Cancel the common factor of $\ln (4)$ .

Cancel the common factor.

$\frac{x \ln (4)}{\ln (4)} = \frac{\ln (6)}{\ln (4)}$

Divide $x$ by $1$ .

$x = \frac{\ln (6)}{\ln (4)}$