Answer:
2/3
Step-by-step explanation:
[tex]log_{27}(9)[/tex]
Let x= [tex]log_{27}(9)[/tex]
Convert it into exponential form
[tex]x= log_b(a)[/tex] can be written as [tex]b^x= a[/tex]
x= [tex]log_{27}(9)[/tex] can be written as [tex]{27}^x= 9[/tex]
27 is 3 times 3 times 3 . its 3^3
9 is 3 times 3 . its 3^2
[tex]{27}^x= 9[/tex]
[tex]{3^3}^x= 3^2[/tex]
[tex]{3}^{3x}= 3^2[/tex]
Base are same so we equate the exponents
[tex]3x= 2[/tex]
Divide both sides by 3
x= 2/3
