SOLUTION: Prove the statement TRUE OR FALSE without calculator. Assume all necessary restrictions hold. m^(log(𝑏)n) = n^(log(𝑏)m)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Prove the statement TRUE OR FALSE without calculator. Assume all necessary restrictions hold. m^(log(𝑏)n) = n^(log(𝑏)m)       Log On


   

Question 1152440: Prove the statement TRUE OR FALSE without calculator. Assume all necessary restrictions hold.
m^(log(𝑏)n) = n^(log(𝑏)m)

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

m%5E%28log%28b%2Cn%29%29+=+n%5E%28log%28b%2Cm%29%29

use log property:
b%5E%28log%28b%2Cx%29+%29=+x for all+x+%3E+0

in your case, left side is
m%5E%28log%28b%2Cn%29%29=> compare to b%5E%28log%28b%2Cx%29+%29=+x
=>b=m, x=n, than you can write it as
m%5E%28log%28m%2Cn%29%29+=+n
do same with right side
n%5E%28log%28b%2Cm%29%29+
=>b=n, x=m
n%5E%28log%28n%2Cm%29%29+=m
so,
m%5E%28log%28b%2Cn%29%29+=+n%5E%28log%28b%2Cm%29%29 would be

n=m =>which is +FALSE+
n%3C%3Em