Answer:
[tex]\log_8{(0.43)}=\boxed{ -0.4059}[/tex]
Step-by-step explanation:
We can solve this problem by using the change of base rule for logarithms which can compute the logarithm of a number to any arbitrary base
The rule is:
[tex]\log_a{x} = \dfrac{\log_{10}{x}}{\log_{10}{a}}[/tex]
Logarithms to the base 10 are easily available in any scientific calculator
In the given problem
x = 0.43
a = 8
[tex]\log_8{0.43} = \dfrac{\log_{10}{(0.43)}}{\log_{10}{(8)}}[/tex]
Using a calculator this works out to: -0.405864 or 0.4059 rounded to 4 decimal places
Answer: [tex]-0.4059[/tex]
