Respuesta :

[tex]\log _{3}(3)=1[/tex] and [tex]\log _{3} \frac{a}{3}=-1.631[/tex]

Solution:

Given value [tex]\log _{3} a=-0.631[/tex].

To evaluate the expression [tex]\log _{3} \frac{a}{3}[/tex].

Using logarithmic rule: [tex]\log _{b}\left(\frac{M}{N}\right)=\log _{b}(M)-\log _{b}(N)[/tex]

[tex]$\log _{3} \frac{a}{3}=\log _{3}(a)-\log _{3}(3)[/tex]

We know that [tex]\log _{3} a=-0.631[/tex].

[tex]$\log _{3} \frac{a}{3}=-0.631-\log _{3}(3)[/tex]

Using another logarithmic rule: [tex]\log _{b} b=1[/tex]

[tex]$\log _{3} \frac{a}{3}=-0.631-1[/tex]

[tex]$\log _{3} \frac{a}{3}=-1.631[/tex]

Hence [tex]\log _{3}(3)=1[/tex] and [tex]\log _{3} \frac{a}{3}=-1.631[/tex].

To solve the problem, the concept of logarithmic must be known.

the value of a and [tex]\rm log_3 (a/3)[/tex] is 0.5 and -1.630.

What is the logarithmic function?

The logarithmic function is the inverse of the exponential function.

Given

[tex]\rm log_3a = -0.634[/tex] is a logarithmic function.

To find

The value of a.

We know the logarithmic property.

[tex]\rm b^{log_ba} =a[/tex]

Then according to the property,

[tex]\begin{aligned} \rm 3^{log_3a} &= 3^{-0.631}\\\\\rm a &= 3^{-0.631}\\\\\rm a &= 0.5\end{aligned}[/tex]

Then

[tex]\rm log_3 \dfrac{a}{3} \\\\\rm log_3 \dfrac{0.5}{3} \\\\\rm log_3 0.167\\\\-1.63[/tex]

Thus, the value of a and [tex]\rm log_3 (a/3)[/tex] is 0.5 and -1.630.

More about the logarithmic function link is given below.

https://brainly.com/question/3072484

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