Question

log a 3=2, why 'a' is irrational? give reason​

Answer 1

'a' is irrational .

Step-by-step explanation:

We have,

$\log_a 3$ = 2

a is a irrational, give reason.

∴ $\log_a 3$ = 2

By logarithm property,

$a^{2}$ = 3

⇒ a = $3^{\dfrac{1}{2} }$

⇒ a = $\sqrt{3}$

$\sqrt{3}$ is an irrational number.

$\sqrt{3}$ is an infinite, non-recurring decimal.

Using a calculator gives:

a =  $\sqrt{3}$  =  1.7320508 ... .

Thus, a is irrational .