Solve the equation: log5 (4x+3)−log5 (x−1)=2.

As both terms on the left hand side have base 5 we know we can combine them. When dealing with logs, a minus means we can divide them, and a plus means we can multiply them. This will leave us with log5(4x+3/x-1)=2. Next we can get rid of the log, we do this by taking 5 squared as this is what the log means. This leaves us with 4x+3/x-1=5^2=25. We can now solve this to find x. 4x+3=25(x-1), expand the brackets: 4x+3=25x-25. Taking all x to one side and constants to the other leaves us with 28=21x. Therefore x=4/3