Question

Show that a⁰ = 1 so logₐ1=0.

Answer 1

Hey there! Thanks for the question!

We know that, Any number except 0 divided by itself gives 1 .

So,

$\frac{ { a}^{m} }{ {a}^{m} } = 1 \\ \\ {a}^{m - m} = 1 \\ \\ {a}^{0} = 1$

We used laws of exponents that ,
$\frac{ {x}^{p} }{ {x}^{q} } = {x}^{p - q}$
So, a^0 = 1

We know that, Logarithmic form of x^n = a is
$log_{x}(a) = n$
where a, x are positive integers .


Now, a^0 = 1

Logarithmic form of a^0 = 1 is
$log_{a}(1) = 0$

Therefore, We proved that a⁰ = 1 so logₐ1=0.