Solve for x 11-4^x=5

$11 - 4^{x} = 5$

Step 1

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

Subtract $11$ from both sides of the equation.

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

Subtract $11$ from $5$ .

$- 4^{x} = - 6$

Step 2

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 3

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

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

Step 4

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

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

Step 5

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 $1$ .

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 1.29248125 \dots$