Question

proof that log 18 base 4 is an irrational number​

Answer 1

$let \: log(18) base4 = x \\ \\ {4}^{x} = 18 \\ \\ there \: is \: no \: value \: for \: x \: to \: get \: 18 \\ so \: it \: is \: irratinal$

Answer 2

To prove : Log 18 base 4 is irrational

Proof :

let it is a rational number

i.e

$log_4 18= \frac{p}{q}$

now,

$4^\frac{p}{q}= 18\\\\ 2^\frac{2p}{q}= 18$

which is never possible

thus the assumption is false

hence , $log_4 18$  is irrational

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