Precalculus Examples

$\log_{3.1419} (64)$

Step 1

Rewrite $\log_{3.1419} (64)$ using the change of base formula.

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Step 1.1

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 $0$ .

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

Step 1.2

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

$\frac{\log (64)}{\log (3.1419)}$

Step 2

Log base $10$ of $3.1419$ is approximately $0.49719235$ .

$\frac{\log (64)}{0.49719235}$

Step 3

Log base $10$ of $64$ is approximately $1.80617997$ .

$\frac{1.80617997}{0.49719235}$

Step 4

Divide $1.80617997$ by $0.49719235$ .

$3.63275891$