SOLUTION: if g(x) = log4 x, find g(8)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: if g(x) = log4 x, find g(8)      Log On


   

Question 417262: if g(x) = log4 x, find g(8)
Answer by jsmallt9(3759) About Me  (Show Source):
You can put this solution on YOUR website!
I assume "log4 x" means log%284%2C+%28x%29%29.

g%288%29+=+log%284%2C+%28%288%29%29%29
Since 4, the base, and 8, the argument, are both powers of 2 (4+=+2%5E2 and 8+=+2%5E3), we will be able find find this logarithm without the use of a calculator. We will use the change of base formula, log%28a%2C+%28p%29%29+=+log%28b%2C+%28p%29%29%2Flog%28b%2C+%28a%29%29, to convert this base 4 log into an expression of base 2 logs: