5-log-2-3-is-transcendental-General-Let-a-b-and-c-algebraic-and-log-b-c-transcendental-If-a-log-b-c-is-algebraic-so-b-a-q-with-q-rational-

Question Number 10912 by geovane10math last updated on 01/Mar/17

5^{\log_{2} 3} is transcendental ?

General :

Let a, b and c algebraic and \log_{b} c

transcendental . If a^{\log_{b} c} is algebraic, so

b = a^{q}, with q rational ?

Commented by FilupS last updated on 03/Mar/17

A transendental number is one that

is non alegebraic

x = 5^{\log_{2} 3}

one method of \log_{b} (c) is trancendental if :

a \neq b (and a is prime)

Facebook Tweet Pin