I will guess that your subject line contains the exercise in question. (This is frequently not the case, which is why it is best to put the entire question inside the post. Thank you.)
To check the solution to any "solving" problem, plug it back in to the original exercise, and see if it works. In your case:
. . . . .Check log<sub>2</sub>(5x - 3) for x = 19/5:
. . . . .log<sub>2</sub>(5[19/5] - 3)
. . . . .log<sub>2</sub>(19 - 3)
. . . . .log<sub>2</sub>(16)
Since the power needed on 2 to get "16" is 4, then log<sub>2</sub>(2) = 4, and the solution is confirmed.
Eliz.