Finite Math Examples

$\ln (2) = 12 t \ln (1.006667)$

Step 1

Rewrite the equation as $12 t \ln (1.006667) = \ln (2)$ .

$12 t \ln (1.006667) = \ln (2)$

Step 2

Divide each term in $12 t \ln (1.006667) = \ln (2)$ by $12 \ln (1.006667)$ and simplify.

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Step 2.1

Divide each term in $12 t \ln (1.006667) = \ln (2)$ by $12 \ln (1.006667)$ .

$\frac{12 t \ln (1.006667)}{12 \ln (1.006667)} = \frac{\ln (2)}{12 \ln (1.006667)}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $12$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{12 t \ln (1.006667)}{12 \ln (1.006667)} = \frac{\ln (2)}{12 \ln (1.006667)}$

Step 2.2.1.2

Rewrite the expression.

$\frac{t \ln (1.006667)}{\ln (1.006667)} = \frac{\ln (2)}{12 \ln (1.006667)}$

Step 2.2.2

Cancel the common factor of $\ln (1.006667)$ .

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Step 2.2.2.1

Cancel the common factor.

$\frac{t \ln (1.006667)}{\ln (1.006667)} = \frac{\ln (2)}{12 \ln (1.006667)}$

Step 2.2.2.2

Divide $t$ by $1$ .

$t = \frac{\ln (2)}{12 \ln (1.006667)}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$t = \frac{\ln (2)}{12 \ln (1.006667)}$

Decimal Form:

$t = 8.69275570 \dots$