Solve 3^2(3^x-10)=0

$$3 ^ { 2 } ( 3 ^ { x } - 10 ) = 0$$

Solve for x

$$x=\log_{3}\left(10\right)\approx 2.095903274$$

Steps Using Definition of Logarithm

Calculate 3 to the power of 2 and get 9.

$$9\left(3^{x}-10\right)=0$$

Use the distributive property to multiply 9 by 3^{x}-10.

$$9\times 3^{x}-90=0$$

Add 90 to both sides of the equation.

$$9\times 3^{x}=90$$

Divide both sides by 9.

$$3^{x}=10$$

Take the logarithm of both sides of the equation.

$$\log(3^{x})=\log(10)$$

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

$$x\log(3)=\log(10)$$

Divide both sides by \log(3).

$$x=\frac{\log(10)}{\log(3)}$$

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

$$x=\log_{3}\left(10\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(3)}+\log_{3}\left(10\right)$$

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