Question 30488: log2*=x
logex=4
Answer by sdmmadam@yahoo.com(530)   (Show Source):
You can put this solution on YOUR website! Probably the problem is
e^x = 4----(1)
Here the base is e, the power is x and the number is 4
Therefore by definition that log(of a positive quantity N) to a given base b is the power p to which the base b has to be raised to give the number N
Therefore x = log[e](4)
Answer: x = log[e](4)
Note: If you do not understand how to apply the definition
you may proceed as follows too
Taking log on both sides of (1) (base e)
log(e^x) =log(4)
xlog[e](e) = log[e](4) (using log[b](m^n) = nlog[b](m) )
That is xX1 = log[e](4)
[since log(any positive quantity) to the same base is 1]
That is x = log[e](4)
Answer: x = log[e](4)
Note: Practising the definition and writing down the answer in a jiffy will really help
Examples
1)log[10](100)= x
means 100 = 10^x = 10^2 and therefore x = 2
2)log[5](125) = t
means 125= 5^x = 5^3 and therefore x = 3
3)log[2](y) = 5
means y = 2^5 = 32
4)log[3](t) = 4
means t = 3^4 = 81
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