Is log4(18) an Irrational Number?

Thread starter CPatCU
Start date Oct 4, 2011
Tags

Irrational

AI Thread Summary

To determine if log4(18) is an irrational number, the discussion focuses on the definition of rational numbers, which are expressed in the form x/y. The equation log4(18) can be rewritten using the change of base formula: log4(18) = log2(18) / log2(4). The attempt at a solution involves setting log2(18) equal to a rational expression, leading to the realization that a proof by contradiction is necessary. The main challenge lies in demonstrating that assuming log4(18) is rational leads to an inconsistency.

Oct 4, 2011

CPatCU

Homework Statement

log₄18
rational numbers are in form x/y

Homework Equations

log_ab = log_cb / log_ca

The Attempt at a Solution

log₂18 / log₂18 = x/y
(b) log₂18 = (a) log₂18
log₂18^b = log₂18^a

Then I am stuck.

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Oct 4, 2011

CPatCU

Sorry, the problem is prove that log(4)18 is irrational. I also realize that this should be done as a contradiction, I am just not sure how to do it.

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