Solve 3*4.85^x=3

$$3 \times { 4.85 }^{ x } =3$$

Solve for x

$$x=0$$

Steps Using Definition of Logarithm

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

$$3\times 4.85^{x}=3$$

Divide both sides by 3.

$$4.85^{x}=1$$

Take the logarithm of both sides of the equation.

$$\log(4.85^{x})=\log(1)$$

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

$$x\log(4.85)=\log(1)$$

Divide both sides by \log(4.85).

$$x=\frac{\log(1)}{\log(4.85)}$$

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

$$x=\log_{4.85}\left(1\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(4.85)}$$

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