Answer:
[tex]\log_{9}(3) = \frac{1}{2}[/tex]
Step-by-step explanation:
To solve logarithms, we have to consider the following:
[tex]\log_{a}(b) = c[/tex] means that [tex]a^{c} = b[/tex].
So, for example:
[tex]\log_{10}(100) = 2[/tex] means that [tex]10^{2} = 100[/tex].
So
[tex]\log_{9}(3) = x[/tex]
[tex]9^{x} = 3^{1}[/tex]
9 is 3*3. So
[tex]3^{2x} = 3^{1}[/tex]
[tex]2x = 1[/tex]
[tex]x = \frac{1}{2}[/tex]
So
[tex]\log_{9}(3) = \frac{1}{2}[/tex]
