Solve 7^x+11=170

$$7 ^ { x } + 11 = 170$$

Solve for x

$$x=\log_{7}\left(159\right)\approx 2.604901467$$

Steps Using Definition of Logarithm

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

$$7^{x}+11=170$$

Subtract 11 from both sides of the equation.

$$7^{x}=159$$

Take the logarithm of both sides of the equation.

$$\log(7^{x})=\log(159)$$

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

$$x\log(7)=\log(159)$$

Divide both sides by \log(7).

$$x=\frac{\log(159)}{\log(7)}$$

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

$$x=\log_{7}\left(159\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(7)}+\log_{7}\left(159\right)$$

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