Solve 4^114^2x=4

$${ 4 }^{ 11 } { 4 }^{ 2x } = 4$$

Solve for x

$$x=-5$$

Steps Using Definition of Logarithm

Use the rules of exponents and logarithms to solve the equation.

$$4194304\times 4^{2x}=4$$

Divide both sides by 4194304.

$$4^{2x}=\frac{1}{1048576}$$

Take the logarithm of both sides of the equation.

$$\log(4^{2x})=\log(\frac{1}{1048576})$$

The logarithm of a number raised to a power is the power times the logarithm of the number.

$$2x\log(4)=\log(\frac{1}{1048576})$$

Divide both sides by \log(4).

$$2x=\frac{\log(\frac{1}{1048576})}{\log(4)}$$

By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$2x=\log_{4}\left(\frac{1}{1048576}\right)$$

Divide both sides by 2.

$$x=-\frac{10}{2}$$

Solve for x (complex solution)

$$x=\frac{\pi n_{1}i}{2\ln(2)}-5$$

$$n_{1}\in \mathrm{Z}$$