Respuesta :

[tex]log_{8} 12 = \frac{ln 12}{ln 8} [/tex]
        = 1.1949 when simplified out
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]