SOLUTION: prove that log<sub>a</sub>m = log<sub>b</sub>m × log<sub>a</sub>b

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: prove that log<sub>a</sub>m = log<sub>b</sub>m × log<sub>a</sub>b      Log On


   

Question 473050: prove that
logam = logbm × logab
Answer by karaoz(32) About Me  (Show Source):
You can put this solution on YOUR website!

Prove that:
logam = logbm × logab

Let
logbm = x
logab = y

We need to show that 
logam = xy

If logab = y then ay = b, and
if logbm = x then bx = m
Substituting b = ay into bx = m, we get
(ay)x = m,
which is the same as:
axy = m.
This means that logam = xy.
We can substitute back the expressions for x and y to see this result in the form requested:
logam = logbm × logab