Question

If loga 3 = 2, why 'a' is irrational ? Give reason.
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Answer 1

The value of a is irrational because it cannot be written as $\dfrac{p}{q}$ form.

Step-by-step explanation:

We have,

$\log_a 3 = 2$

a' is irrational ? Gi

∴ $\log_a 3 = 2$

By logarithm property,

⇒ $a^2=3$

⇒ $a=\sqrt{3}$

⇒ a = 1.7305.....

It cannot be written as $\dfrac{p}{q}$ form, where q ≠ 0.

Thus, the value of a is irrational because it cannot be written as $\dfrac{p}{q}$ form.