Solve 5^x-3=6

$$5 ^ { x } - 3 = 6$$

Solve for x

$$x=2\log_{5}\left(3\right)\approx 1.365212389$$

Steps Using Definition of Logarithm

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

$$5^{x}-3=6$$

Add 3 to both sides of the equation.

$$5^{x}=9$$

Take the logarithm of both sides of the equation.

$$\log(5^{x})=\log(9)$$

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

$$x\log(5)=\log(9)$$

Divide both sides by \log(5).

$$x=\frac{\log(9)}{\log(5)}$$

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

$$x=\log_{5}\left(9\right)$$

Solve for x (complex solution)

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

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