If the sum is 2^x = 8, how do I work out x?
When I use my calculator, I press 'log', then 2 and then in brackets (8), so it looks like this "log2(8)". Why do I get the answer of 2.4082399.....
There are a lot of different ways to solve this equation. I'm going to show you 2 of them:
1. Change 8 into a power of 2:
$\displaystyle 2^x = 8~\implies~2^x=2^3$
Two powers of the same base are equal if the exponents are equal too.
2. Use logarithms (but correct) and the base-change-formula:
$\displaystyle 2^x = 8~\implies~x=\log_2(8) ~\implies~x=\dfrac{\log(8)}{\log(2)} = \dfrac{\ln(8)}{\ln(2)}$
Using logs you can say
$\displaystyle \displaystyle 2^x = 8$
$\displaystyle \displaystyle \log_22^x = \log_28$
$\displaystyle \displaystyle x = \log_22^3$
$\displaystyle \displaystyle x = 3\log_22$
$\displaystyle \displaystyle x = 3\times 1 $
$\displaystyle \displaystyle x = 3 $
Seems like the long way home though, do you agree?