Question

Solve for x:

logx+log(x-1)=log(4x)
i got x=5 ... is this correct?

Answer 1

x^2-x = 4x
x^2-5x=0
x(x-5) = 0
it's 0 or 5 but since you can't have a negative inside the log,
answer is five.
correct :D

Answer 2

thank you!!!

Answer 3

here log(x(x-1))=log4x
or x(x-1)=4x
or x^2-x=4x
or x^2 -5x=0
hence x(x-5)=0
hence x=0 or x=5
but if x=0 we have log(x-1)=log(-1) (absurd as we cannot take log of negatives)
hence x=5