Basic Math Examples

$20024 = 13800^{(r) (6)}$

Step 1

Rewrite the equation as $13800^{(r) (6)} = 20024$ .

$13800^{(r) (6)} = 20024$

Step 2

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (13800^{(r) (6)}) = \ln (20024)$

Step 3

Expand the left side.

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Step 3.1

Expand $\ln (13800^{(r) (6)})$ by moving $(r) (6)$ outside the logarithm.

$(r) (6) \ln (13800) = \ln (20024)$

Step 3.2

Multiply $r$ by $6$ .

$r (6) \ln (13800) = \ln (20024)$

Step 4

Simplify the left side.

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Step 4.1

Move $6$ to the left of $r$ .

$6 r \ln (13800) = \ln (20024)$

Step 5

Divide each term in $6 r \ln (13800) = \ln (20024)$ by $6 \ln (13800)$ and simplify.

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Step 5.1

Divide each term in $6 r \ln (13800) = \ln (20024)$ by $6 \ln (13800)$ .

$\frac{6 r \ln (13800)}{6 \ln (13800)} = \frac{\ln (20024)}{6 \ln (13800)}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $6$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{6 r \ln (13800)}{6 \ln (13800)} = \frac{\ln (20024)}{6 \ln (13800)}$

Step 5.2.1.2

Rewrite the expression.

$\frac{r \ln (13800)}{\ln (13800)} = \frac{\ln (20024)}{6 \ln (13800)}$

Step 5.2.2

Cancel the common factor of $\ln (13800)$ .

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Step 5.2.2.1

Cancel the common factor.

$\frac{r \ln (13800)}{\ln (13800)} = \frac{\ln (20024)}{6 \ln (13800)}$

Step 5.2.2.2

Divide $r$ by $1$ .

$r = \frac{\ln (20024)}{6 \ln (13800)}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$r = \frac{\ln (20024)}{6 \ln (13800)}$

Decimal Form:

$r = 0.17317538 \dots$