Solve 2(3^x)=40

$$2( { 3 }^{ x } )=40$$

Solve for x

$$x=\log_{3}\left(20\right)\approx 2.726833028$$

Steps Using Definition of Logarithm

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

$$2\times 3^{x}=40$$

Divide both sides by 2.

$$3^{x}=20$$

Take the logarithm of both sides of the equation.

$$\log(3^{x})=\log(20)$$

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

$$x\log(3)=\log(20)$$

Divide both sides by \log(3).

$$x=\frac{\log(20)}{\log(3)}$$

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

$$x=\log_{3}\left(20\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(3)}+\log_{3}\left(20\right)$$

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