How do you write a^2 = 36 in log form?

May 9, 2016

In this form, $a = \pm 6$. The logarithmic form is ${\log}_{a} 36 = 2$ and, solving this, a = 6..

Explanation:

If $x = {b}^{y}$, the inverse relation is $y = {\log}_{b} x$.

Here, x = 36, b = a and y = 2.

So, ${\log}_{a} 36 = {\log}_{a} \left({6}^{2}\right) = 2 {\log}_{a} 6 = 2$.

Now, ${\log}_{a} 6 = 1$. So, a = 6, as ${\log}_{a} a = 1$..