Solve 3*9^x-9^x=6

$$3 \cdot 9 ^ { x } - 9 ^ { x } = 6$$

Solve for x

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

Steps Using Definition of Logarithm

Combine 3\times 9^{x} and -9^{x} to get 2\times 9^{x}.

$$2\times 9^{x}=6$$

Divide both sides by 2.

$$9^{x}=\frac{6}{2}$$

Divide 6 by 2 to get 3.

$$9^{x}=3$$

Take the logarithm of both sides of the equation.

$$\log(9^{x})=\log(3)$$

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

$$x\log(9)=\log(3)$$

Divide both sides by \log(9).

$$x=\frac{\log(3)}{\log(9)}$$

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

$$x=\log_{9}\left(3\right)$$

Solve for x (complex solution)

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

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