Here is the problem:

5

^{2x+1}= 7

^{3-x}

The steps follow:

2x+1 = (3-x) log

_{5}7

What he does next with the (3-x) is what really throws me:

2x+1 = 3 log

_{5}7 - x log

_{5}7

2x + x log

_{5}7 = 3 log

_{5}7 - 1

x(2 + log

_{5}7) = 3 log

_{5}7 - 1

The answer is:

x = 3 log

_{5}7 -1

- 2 + log

_{5}7

Again, I was with him until the right side of the second step where things started happening that I cant figure out. Thanks for the help.