Question

Solve the equation below for x:
Log2x+log(2x-1) = log3x

a. there are no solutions
b. x=0,5/4
c. x=5/4
d. x=5/2

Answer 1

\[\log2x+\log(2x-1)=\log3x\\
\log(2x(2x-1))=\log3x\\
4x^2-2x=3x\\
x=\cdots\]
Be careful as to what you call your solution. Since \(\log x\) is defined for \(x>0\) only, you have to make sure that your solution works, i.e. \(2x>0,~2x-1>0,~3x>0\), or more simply, \(x>\dfrac{1}{2}\).