Solve (11)^x=10

$$( 11 ) ^ { x } = 10$$

Solve for x

$$x=\log_{11}\left(10\right)\approx 0.960252568$$

Steps Using Definition of Logarithm

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

$$11^{x}=10$$

Take the logarithm of both sides of the equation.

$$\log(11^{x})=\log(10)$$

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

$$x\log(11)=\log(10)$$

Divide both sides by \log(11).

$$x=\frac{\log(10)}{\log(11)}$$

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

$$x=\log_{11}\left(10\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(11)}+\log_{11}\left(10\right)$$

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