Change of Base Formula

Since we are using logarithms more now I figured this would be beneficial to know. The change of base formula is used as follows:

2^x = 5
Log (2^x) = Log (5)
x Log (2) = Log (5)
x = ^{Log (5)}⁄_{Log (2)}
x = 2.32

The reason for this is a law of logarithms. The law states that Log (x^a) is equal to a*Log (x). Because of this we can change Log (2^x) into x*Log (2). Once we change it into simple multiplication we just have to divide it on both sides of the equation. That gives us the value of x when we don't have like bases.