If 8^m = 32 then what is the value of m?

Question

If a , b , c are positive real numbers such that

a(b+c) = 32
b(c+a) = 65
c(a+b) = 77

Find the value of a*b*c

Answer 1

8 ^ m =32
( 2^ 3) ^ m =32
2 ^ (3 * m) =32
2 ^ (3m) =( 2^ 5)
2 ^(3m) = 2 ^ 5

on comparing 3m=5
=>

    m= 5 /3

Answer 2

8^m=32 ---> m log8=log32 --->3m log2 = 5 log2 ---> 3m=5 so m=5/3