How do you evaluate log_3 1?

Aug 15, 2016

I found that it is equal to zero:

Explanation:

You may use the definition of log:
${\log}_{b} a = x$
so that: $a = {b}^{x}$

we now need to find our $x$ in:
${\log}_{3} \left(1\right) = x$

using our definition we see that the only possible value for $x$ is zero because:
$1 = {3}^{0}$

Aug 15, 2016

${\log}_{3} 1 = 0$

Explanation:

Written in log form, the question being asked is,"

"1 is which power of 3? " ${3}^{0} = 1$

Or

"Using a base of 3, what index will give 1 as the answer?"
${3}^{0} = 1$

Log form and index form are interchangeable.

${\log}_{3} 1 = x \text{ } \Rightarrow {3}^{x} = 1$

$x = 0$