6^x = 5 equation, how to solve it?

Question

If it would be 6^x = 1 or 6^x = 6 or 6^x = 36 it would be extremely easy, but how to solve this equation:
6^x = 5
I don't need an answer, I want to find out how to solve equations like this one, I need solution.
Thanks.

Answer 1

x = log(5) / log(6)

Answer 2

Use the logarithm with an appropriate base.

Answer 3

Solve[6^x == 5, x]

See Wolfram Alpha do this here: http://www.wolframalpha.com/input/?i=Solve[6^x+%3D%3D+5,+x]

Also take a look at http://reference.wolfram.com/mathematica/tutorial/SolvingEquations.html

Answer 4

Take logs of both sides:

log(6^x) = log(5)

Simplify using standard log rules:

x log(6) = log(5)

Divide:

x = log(5) / log(6)

Doesn't matter what base you take.