Solve 1400=2*3^n

$$1400 = 2 \cdot 3 ^ { n }$$

Solve for n

$$n=\log_{3}\left(700\right)\approx 5.963050298$$

Steps Using Definition of Logarithm

Divide both sides by 2.

$$\frac{1400}{2}=3^{n}$$

Divide 1400 by 2 to get 700.

$$700=3^{n}$$

Swap sides so that all variable terms are on the left hand side.

$$3^{n}=700$$

Take the logarithm of both sides of the equation.

$$\log(3^{n})=\log(700)$$

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

$$n\log(3)=\log(700)$$

Divide both sides by \log(3).

$$n=\frac{\log(700)}{\log(3)}$$

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

$$n=\log_{3}\left(700\right)$$