When are you supposed to take the natural log of both sides of an equation

It seems this is done randomly, but when do you know to do it? What is like a clue or the rules that indicate you can/should take the natural log of both sides of an equation?

You take the natural log of both sides when e is raised to a variable power. For example,
e^x = 10
ln(e^x) = ln10
x = ln10

you can also take the natural log of both sides when you have two different bases

5^x = 3^(2x - 5)
ln (5^x) = ln 3^(2x - 5) ==>
x ln 5 = (2x - 5) ln 3 = 2x ln 3 - 5 ln 3
5 ln 3 = 2x ln 3 - x ln 5 = x (2 ln 3 - ln 5)
x = 5 ln 3 / (2 ln 3 - ln 5)

Report Abuse