SOLUTION: If {{{ log (a,2) = log(b,8) }}}, show that a^3 = b

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: If {{{ log (a,2) = log(b,8) }}}, show that a^3 = b      Log On


   

Question 614573: If +log+%28a%2C2%29+=+log%28b%2C8%29+, show that a^3 = b
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
loga(2) = logb(8) = n

a^n = 2 ___(a^n)^3 = 2^3 ___ a^(3n) = 8

b^n = 8

substituting ___ a^(3n) = b^n

[a^(3n)]^(1/n) = (b^n)^(1/n)

a^3 = b