Answer-
Using the change of base rule, the value of [tex]\log_8 0.082[/tex] was found to be -1.2027
Solution-
Change of base rule,
[tex]\log_y x=\frac{\log_a x}{\log_a y}[/tex]
where, a is the new base.
Here,
x = 0.082 and y = 8
Taking a=10 in this case,
[tex]\log_8 0.082=\frac{\log_10 0.082}{\log_10 8}[/tex]
[tex]=\frac{-1.0861}{0.9030}[/tex]
[tex]=-1.2027[/tex]
The value of 'a' really does not matter. Taking different bases will yield the same result, because at the end we are taking the ratio.
