Math, asked by gyan69, 1 year ago

proof that log 18 base 4 is an irrational number​

Answers

Answered by maheshv22
10

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

Answered by TanikaWaddle
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

#Learn more :

https://brainly.in/question/7539604

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