Solve 121^4x=11

$$121 ^ { 4 x } = 11$$

Solve for x

$$x=\frac{1}{8}=0.125$$

Steps Using Definition of Logarithm

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

$$121^{4x}=11$$

Take the logarithm of both sides of the equation.

$$\log(121^{4x})=\log(11)$$

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

$$4x\log(121)=\log(11)$$

Divide both sides by \log(121).

$$4x=\frac{\log(11)}{\log(121)}$$

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

$$4x=\log_{121}\left(11\right)$$

Divide both sides by 4.

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

Solve for x (complex solution)

$$x=\frac{i\pi n_{1}}{4\ln(11)}+\frac{1}{8}$$

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