MIT 8.01 Physics I Classical Mechanics, Fall 1999 OpenStudy (anonymous):

Prove that log4(9) is irrational. I have no idea where to even begin on that. OpenStudy (anonymous):

is it log of 9 to the base 4? if it is then here is the solution though i m not sure whether this correct or incorrect.... log3^2 to the base 2^2 so the eqn becomes 2/2log2(3) [log of 3 to the base 2] =>log2(3) =>ln3/ln2 [using base change property] now let this be a rat. no. of the form p/q =>ln3/ln2=p/q =>q(ln3)=p(ln2) =>ln3^q=ln2^p cancelling ln from both the sides; 3^q=2^p......(1) But 3^q is always gonna be odd n 2^p is always gonna be even. So this contradicts the eqn (1). So log4(9) is irrational. OpenStudy (anonymous):

That's the route I took! Thanks for the reply!

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