Respuesta :

carlosego

Answer: option a.

Step-by-step explanation:

 By definition we know that:

 [tex]log_a(a^n)=n[/tex]

Where a is the base of the logarithm.

 We also know that:

[tex]\sqrt{x}=x^{\frac{1}{2}}[/tex]

Then you can rewrite the logarithm given in the problem, as you can see below:

[tex]log_{17}(\sqrt{17})[/tex]

And keeping on mind the property, you obtain:

[tex]=log_{17}(17^{\frac{1}{2}})=\frac{1}{2}[/tex]

Therefore, you can conclude that the answer is the option a.

Ashraf82

Answer:

The answer is 1/2 ⇒ answer (a)

Step-by-step explanation:

*The logarithm function is the inverse of the exponential function

- Ex: If 2³ = 8 ⇒  then [tex]log_{2}(8) = 3[/tex]

 Vice versa : If [tex]log_{5}(125)=3[/tex] ⇒ 5³ = 125

* In logarithm function:

- If [tex]log_{a}a=1[/tex] because [tex]a^{1}=a[/tex]

- If [tex]log_{a}a^{n}=(n)log_{a}a=n[/tex]

∵ [tex]log_{17}\sqrt{17}=log_{17}(17)^{\frac{1}{2}}[/tex]

- √b = [tex]b^{\frac{1}{2}}[/tex]

∴ [tex]log_{17}(17)^{\frac{1}{2}}=\frac{1}{2}log _{17}(17)=\frac{1}{2}(1) = \frac{1}{2}[/tex]

∴ The answer is 1/2 ⇒ answer (a)

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