Evaluate ( log of t)/( log base 8 of t)

$\frac{\log (t)}{\log_{8} (t)}$

Rewrite $\log_{8} (t)$ using the change of base formula.

The change of base rule can be used if $a$ and $b$ are greater than $0$ and not equal to $1$ , and $x$ is greater than $0$ .

$\frac{\log (t)}{\log_{a} (x) = \frac{\log_{b} (x)}{\log_{b} (a)}}$

Substitute in values for the variables in the change of base formula, using $b = 10$ .

$\frac{\log (t)}{\frac{\log (t)}{\log (8)}}$

Multiply the numerator by the reciprocal of the denominator.

$\log (t) \frac{\log (8)}{\log (t)}$

Cancel the common factor of $\log (t)$ .

Cancel the common factor.

$\log (t) \frac{\log (8)}{\log (t)}$

Rewrite the expression.

$\log (8)$

The result can be shown in multiple forms.

Exact Form:

$\log (8)$

Decimal Form:

$0.90308998 \dots$