7^x^2=9^x
how do i solve this using logs

Apply lg on both sides.
lg7^x^2 = lg9^x
Bring the power forward.
x^2lg7 = xlg9
x^2/x = lg9/lg7
x = lg9/lg7 = 1.13

Consider for a moment building a tree with all possible choices. The first row would contain 8 books (each possible choice for the first book). Then, the second row would contain 7 books for each book in the first row (the choices possible for the second book). Otherwise, it would be 8*7. Following this principal, we continue to multiply down to 1. 8*7*6*5*4*3*2*1. This is also known as 8!, a factorial.
Finally, 8! = 40,320