Solve 2(3^n)=5

$$2 ( 3 ^ { n } ) = 5$$

Solve for n

$$n=\log_{3}\left(\frac{5}{2}\right)\approx 0.834043767$$

Steps Using Definition of Logarithm

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

$$2\times 3^{n}=5$$

Divide both sides by 2.

$$3^{n}=\frac{5}{2}$$

Take the logarithm of both sides of the equation.

$$\log(3^{n})=\log(\frac{5}{2})$$

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

$$n\log(3)=\log(\frac{5}{2})$$

Divide both sides by \log(3).

$$n=\frac{\log(\frac{5}{2})}{\log(3)}$$

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

$$n=\log_{3}\left(\frac{5}{2}\right)$$