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.
