Precalculus Examples

$3^{3} \log_{3} (2 + 2)$

Step 1

Raise $3$ to the power of $3$ .

$27 \log_{3} (2 + 2)$

Step 2

Add $2$ and $2$ .

$27 \log_{3} (4)$

Step 3

Simplify $27 \log_{3} (4)$ by moving $27$ inside the logarithm.

$\log_{3} (4^{27})$

Step 4

Raise $4$ to the power of $27$ .

$\log_{3} (18014398509482000)$

Step 5

Rewrite $\log_{3} (18014398509482000)$ using the change of base formula.

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Step 5.1

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 5.2

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

$\frac{\log (18014398509482000)}{\log (3)}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{\log (18014398509482000)}{\log (3)}$

Decimal Form:

$34.07020669 \dots$