bagofmud7680 bagofmud7680
  • 22-10-2019
  • Mathematics
contestada

18. Calculate the following logarithms.
c. log9(3)

Respuesta :

joaobezerra joaobezerra
  • 22-10-2019

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]

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