Respuesta :

The value of the given expression in terms of s will be [(s + 0.602)/3].

What is a logarithm?

Exponents can also be written as logarithms. A number base logarithm is similar to some other number. It is the exact inverse of the exponent expression.

If [tex]\log(16) = s[/tex]

Then the value of the given expression in terms of s is given below.

[tex]\dfrac{2}{3} \times \log(6400) - \dfrac{1}{3} \times \log(1600)[/tex]

We know the property of the logarithm.

[tex]\log 100 = 2[/tex]

Then we have

[tex]\rm \rightarrow \dfrac{2}{3} \times \log(6400) - \dfrac{1}{3} \times \log(1600)\\\\\\\rightarrow \dfrac{2}{3} \times ( \log 16 + \log 4 + \log 100 ) - \dfrac{1}{3} \times (\log 16 + \log 100)\\\\\\\rightarrow \dfrac{2}{3} \times (s + 0.602+2) - \dfrac{1}{3} \times (s + 2)\\\\\\\rightarrow \dfrac{2}{3} \times (s + 2.602 ) - \dfrac{1}{3} \times (s + 2)\\\\\\\rightarrow \dfrac{2 (s + 2.602) - (s - 2)}{3} \\\\\\\rightarrow \dfrac{s + 0.602}{3}[/tex]

More about the logarithm link is given below.

https://brainly.com/question/7302008

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