Solve 8^x-7=7

$$8 ^ { x - 7 } = 7$$

Solve for x

$$x = \frac{\log_{2} {(7)} + 21}{3} \approx 7.935784974$$

Steps Using Definition of Logarithm

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

$$8^{x-7}=7$$

Take the logarithm of both sides of the equation.

$$\log(8^{x-7})=\log(7)$$

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

$$\left(x-7\right)\log(8)=\log(7)$$

Divide both sides by \log(8).

$$x-7=\frac{\log(7)}{\log(8)}$$

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

$$x-7=\log_{8}\left(7\right)$$

Add 7 to both sides of the equation.

$$x=\frac{\log_{2}\left(7\right)}{3}-\left(-7\right)$$