Answer:
2/3
Step-by-step explanation:
[tex]log_{27}(9)[/tex]
WE have base 27
LEts apply change of base formula
[tex]log_b(a)=\frac{log a}{log b}[/tex]
[tex]log_{27}(9)=\frac{log 9}{log 27}[/tex]
Now we write 27 and 9 in exponential form
[tex]log_{27}(9)=\frac{log 3^2}{log 3^3}[/tex]
Use power property and move the exponent before log
[tex]log_{27}(9)=\frac{2log 3}{3log 3}[/tex]
canel out log 3 at the top and bottom
[tex]log_{27}(9)=\frac{2}{3}[/tex]
