Respuesta :
If you consider the logarithm base 3 of both sides, you have
[tex] \log_3(3^c) = \log_3(27) [/tex]
You can use a rule of logarithms that allow you to turn exponents into multiplicative factors:
[tex] \log_a(b^c) = c\log_a(b) [/tex]
So the equation becomes
[tex] c\log_3(3)=\log_3(27) [/tex]
Now, by definition, you have
[tex] \log_a(b)=c \iff a^c=b [/tex]
So, you have
[tex] \log_3(3)=x \iff 3^x=3 \iff x = 1,\quad \log_3(27)=y \iff 3^y=27\iff y=3 [/tex]
So, the equation becomes
[tex] 1\cdot c = 3 \iff c=3 [/tex]
[tex]log_{3}[/tex]27 = c
using the law of logs : [tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
given [tex]3^{c}[/tex] = 27 then
[tex]log_{3}[/tex] 27 = c
