Solve 5^x+3=7

$$5 ^ { x + 3 } = 7$$

Solve for x

$$x=\log_{5}\left(7\right)-3\approx -1.790938045$$

Steps Using Definition of Logarithm

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

$$5^{x+3}=7$$

Take the logarithm of both sides of the equation.

$$\log(5^{x+3})=\log(7)$$

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

$$\left(x+3\right)\log(5)=\log(7)$$

Divide both sides by \log(5).

$$x+3=\frac{\log(7)}{\log(5)}$$

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

$$x+3=\log_{5}\left(7\right)$$

Subtract 3 from both sides of the equation.

$$x=\log_{5}\left(7\right)-3$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(5)}+\log_{5}\left(7\right)-3$$

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