SOLUTION: log(base 16) x + log(base 4 x + log(base 2) x = 7 the answer is 16, but i want to know how they got it because i keep getting 16^1/3

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: log(base 16) x + log(base 4 x + log(base 2) x = 7 the answer is 16, but i want to know how they got it because i keep getting 16^1/3      Log On


   

Question 516126: log(base 16) x + log(base 4 x + log(base 2) x = 7
the answer is 16, but i want to know how they got it because i keep getting 16^1/3
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
16 = 2^4 ___ log2(x) = 4[log16(x)]

16 = 4^2 ___ log4(x) = 2[log16(x)]

log16(x) + 2[log16(x)] + 4[log16(x)] = 7

7[log16(x)] = 7

log16(x) = 1

x = 16