[tex]\log50+\log\dfrac x2=2[/tex]
Condense the logarithms on the left into one:
[tex]\log\left(50\cdot\dfrac x2\right)=\log(25x)=2[/tex]
Assuming the base of the logarithm is 10, write both sides as powers of 10. This lets us eliminate the logarithm:
[tex]10^{\log(25x)}=10^2\implies25x=100[/tex]
Divide both sides by 24 to solve for [tex]x[/tex]:
[tex]x=\dfrac{100}4\implies\boxed{x=25}[/tex]
