Solve 3*9^x+1=81

$$3 \times { 9 }^{ x+1 } =81$$

Solve for x

$$x=\frac{1}{2}=0.5$$

Steps Using Definition of Logarithm

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

$$3\times 9^{x+1}=81$$

Divide both sides by 3.

$$9^{x+1}=27$$

Take the logarithm of both sides of the equation.

$$\log(9^{x+1})=\log(27)$$

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

$$\left(x+1\right)\log(9)=\log(27)$$

Divide both sides by \log(9).

$$x+1=\frac{\log(27)}{\log(9)}$$

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

$$x+1=\log_{9}\left(27\right)$$

Subtract 1 from both sides of the equation.

$$x=\frac{3}{2}-1$$

Solve for x (complex solution)

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

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