Question

Loga3 =2 ,why a is irrational?give reason

Answer 1

$log_{a} \: {3} = 2 \: (given)$

$Express\: it \: into \: exponential \: form$

$\implies a^{2} = 3$

$\boxed { \pink { If \: log_{a} {x} = N \implies a^{N} = x }}$

$\implies a = \sqrt{3}$

$\blue { ( Irrational \: number ) }$

Therefore.,

$\red{ log_{a} \: {3} = 2}$

$\green { \blue {\:is \:an \: Irrational \: number } }$

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