Respuesta :
Answer:
The answer is 3/4
Step-by-step explanation:
Hi, we need to change the base of the logarithm, for that we need to use the following formula.
[tex]Log_{b} (a)=\frac{Ln(a)}{Ln(b)}[/tex]
In our case, this is:
[tex]Log_{9} (\sqrt{27} )=\frac{Ln(\sqrt{27} )}{Ln(9)}[/tex]
Which is the same as:
[tex]\frac{Ln(27)^{\frac{1}{2} }}{Ln(9)}[/tex]
Now, let´s solve this using the log properties
[tex]\frac{1}{2} (\frac{Ln(27)}{Ln(9)} )[/tex]
[tex]\frac{1}{2} (\frac{Ln(9*3)}{Ln(9)} )[/tex]
[tex]\frac{1}{2} (\frac{Ln(9)+Ln(3)}{Ln(9)} )[/tex]
[tex]\frac{1}{2} (\frac{Ln(9)}{Ln(9)}+\frac{Ln(3)}{Ln(9)} )\\[/tex]
We can change 3 for 9^(1/2)
[tex]\frac{1}{2} (\frac{Ln(9)}{Ln(9)}+\frac{Ln(9^{\frac{1}{2} } )}{Ln(9)} )\\[/tex]
[tex]\frac{1}{2} (\frac{Ln(9)}{Ln(9)}+\frac{Ln(9 )}{2*Ln(9)} )\\[/tex]
Since Ln(9) / Ln(9) =1, we get.
[tex]\frac{1}{2} (1+\frac{1}{2} )[/tex]
[tex]\frac{1}{2} (\frac{3}{2} )=\frac{3}{4}[/tex]
Best of luck.
