What is the error in this simple logarithmic equation?

[Ali Asadullah]

Can anyone please tell me what is wrong with this solution


log(5x-17) = log(4x-14)
As logarithmic functions are one-one so,
5x-17 = 4x-14
=> x =3

 

[uart]

That's a very good question Ali. The problem is the domain of the log function over the reals.

So there is no solution over the domain of real numbers, however x=3 is a solution if the domain is the complex number field. This is an interesting result in the sense that we require the existence of complex numbers in order for a solution to exist, even though the solution itself is not complex!

 

[elibj123]

What's basically wrong is that neither of the logarithms (in their real sense) are defined for x=3 since their argument will be negative. Comes in what uart said.