Given:
The value is [tex]\log_90.877[/tex].
To find:
The logarithm to four decimal places using the change of base rule.
Solution:
We have,
[tex]\log_90.877[/tex]
Using the change of base rule, we get
[tex]\log_90.877=\dfrac{\log_{10}0.877}{\log_{10}9}[/tex] [tex][\because \log_yx=\dfrac{\log_ax}{\log_ay}][/tex]
[tex]\log_90.877=\dfrac{-0.057000}{0.9542425}[/tex]
[tex]\log_90.877=-0.0597332439081[/tex]
Round the value to the four decimal places.
[tex]\log_90.877\approx -0.0597[/tex]
Therefore, the required value is -0.0597.
