Finite Math Examples

$720000 = 240000 {(0.09)}^{t}$

Step 1

Rewrite the equation as $240000 \cdot {0.09}^{t} = 720000$ .

$240000 \cdot {0.09}^{t} = 720000$

Step 2

Divide each term in $240000 \cdot {0.09}^{t} = 720000$ by $240000$ and simplify.

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Step 2.1

Divide each term in $240000 \cdot {0.09}^{t} = 720000$ by $240000$ .

$\frac{240000 \cdot {0.09}^{t}}{240000} = \frac{720000}{240000}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $240000$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{240000 \cdot {0.09}^{t}}{240000} = \frac{720000}{240000}$

Step 2.2.1.2

Divide ${0.09}^{t}$ by $1$ .

${0.09}^{t} = \frac{720000}{240000}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $720000$ by $240000$ .

${0.09}^{t} = 3$

Step 3

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

$\ln ({0.09}^{t}) = \ln (3)$

Step 4

Expand $\ln ({0.09}^{t})$ by moving $t$ outside the logarithm.

$t \ln (0.09) = \ln (3)$

Step 5

Divide each term in $t \ln (0.09) = \ln (3)$ by $\ln (0.09)$ and simplify.

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Step 5.1

Divide each term in $t \ln (0.09) = \ln (3)$ by $\ln (0.09)$ .

$\frac{t \ln (0.09)}{\ln (0.09)} = \frac{\ln (3)}{\ln (0.09)}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $\ln (0.09)$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{t \ln (0.09)}{\ln (0.09)} = \frac{\ln (3)}{\ln (0.09)}$

Step 5.2.1.2

Divide $t$ by $1$ .

$t = \frac{\ln (3)}{\ln (0.09)}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$t = \frac{\ln (3)}{\ln (0.09)}$

Decimal Form:

$t = - 0.45624464 \dots$