Solve 7^x-2=4

$$7 ^ { x - 2 } = 4$$

Solve for x

$$x=2\left(\log_{7}\left(2\right)+1\right)\approx 2.712414374$$

Steps Using Definition of Logarithm

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

$$7^{x-2}=4$$

Take the logarithm of both sides of the equation.

$$\log(7^{x-2})=\log(4)$$

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

$$\left(x-2\right)\log(7)=\log(4)$$

Divide both sides by \log(7).

$$x-2=\frac{\log(4)}{\log(7)}$$

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

$$x-2=\log_{7}\left(4\right)$$

Add 2 to both sides of the equation.

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