Math log problem is hard

2log(subscript A)X - 1/3log(subscript A)(x-2) - 5log(subscript A) (2x+3)

write the expression as one logarithm

please help i have a midterm tomorrow and this question is so hard !

The subscript A which you have written is known as the base. As they are the same in each case this is quite easy to simplify into one log expression using simple log laws. If you add logs together you multiply e.g log(A)X + log(A)Y = log(A)XY, when you subtract you divide e.g
log(A)X - log(A)Y = log(A)X/Y
also one other log rule is that if there is a number (co-efficient) in front of the log then you raise it as a power e.g Xlog(A)Y = log(A)(Y^X)

to simplify bring all of the powers up as in the last law i showed.
log(A)X^2 - log(A)(x-2)^1/3 - log(A)(2x+3)^5
using the subtraction law
log(A)X^2/(x-2)^1/3 - log (A)(2x + 3)^5
using the subtraction law again
log(A)[(X^2/(x-2)^1/3)/(2x + 3)^5]
= log(A)[X^2/((x-2)^1/3)*(2x+3)^5]