Respuesta :
ANSWER
[tex] \boxed { log_{8}(12) = 1.1950}[/tex]
EXPLANATION
We want to evaluate
[tex] log_{8}(12) [/tex]
This logarithm is in base 8.
Recall the change of base formula,
[tex] log_{a}(b) = \frac{ log_{c}(b) }{ log_{c}(a) } [/tex]
We can change to base e to obtain,
[tex] log_{8}(12) = \frac{ log_{e}(12) }{ log_{e}(8) } [/tex]
[tex] log_{8}(12) = \frac{ ln(12) }{ ln(8) } [/tex]
[tex] log_{8}(12) = \frac{ 2.485}{ 2.079 } [/tex]
[tex] log_{8}(12) = 1.1950[/tex]
[tex] \boxed { log_{8}(12) = 1.1950}[/tex]
EXPLANATION
We want to evaluate
[tex] log_{8}(12) [/tex]
This logarithm is in base 8.
Recall the change of base formula,
[tex] log_{a}(b) = \frac{ log_{c}(b) }{ log_{c}(a) } [/tex]
We can change to base e to obtain,
[tex] log_{8}(12) = \frac{ log_{e}(12) }{ log_{e}(8) } [/tex]
[tex] log_{8}(12) = \frac{ ln(12) }{ ln(8) } [/tex]
[tex] log_{8}(12) = \frac{ 2.485}{ 2.079 } [/tex]
[tex] log_{8}(12) = 1.1950[/tex]