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Given that log_{a}(3) = 0.477 and
log_{a}(5) = 0.699, evaluate log_{a}(0.6) .​

*The answer is -0.222 but I'm not sure how to do the steps.

Sagot :

Given:

[tex]\log_{a}(3) = 0.477,\log_{a}(5) = 0.699[/tex]

To find:

The value of [tex]\log_{a}(0.6)[/tex].

Solution:

We need to find the value of:

[tex]\log_{a}(0.6)[/tex]

It can be written as

[tex]\log_{a}(0.6)=\log_a\left(\dfrac{6}{10}\right)[/tex]

[tex]\log_{a}(0.6)=\log_a\left(\dfrac{3}{5}\right)[/tex]

By using the property of logarithm, we get

[tex]\log_{a}(0.6)=\log_a(3)-\log_a(5)[/tex]        [tex][\because \log \dfrac{a}{b}=\log a-\log b][/tex]

[tex]\log_{a}(0.6)=\log_a(3)-\log_a(5)[/tex]

On substituting the given values, we get

[tex]\log_{a}(0.6)=0.477-0.699[/tex]

[tex]\log_{a}(0.6)=-0.222[/tex]

Therefore, the values of [tex]\log_a(0.6)[/tex] is -0.222.

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