Pre-Algebra Examples

$240000 = 80000 {(1.08)}^{t}$

Step 1

Rewrite the equation as $80000 \cdot {1.08}^{t} = 240000$ .

$80000 \cdot {1.08}^{t} = 240000$

Step 2

Divide each term in $80000 \cdot {1.08}^{t} = 240000$ by $80000$ and simplify.

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Step 2.1

Divide each term in $80000 \cdot {1.08}^{t} = 240000$ by $80000$ .

$\frac{80000 \cdot {1.08}^{t}}{80000} = \frac{240000}{80000}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $80000$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{80000 \cdot {1.08}^{t}}{80000} = \frac{240000}{80000}$

Step 2.2.1.2

Divide ${1.08}^{t}$ by $1$ .

${1.08}^{t} = \frac{240000}{80000}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $240000$ by $80000$ .

${1.08}^{t} = 3$

Step 3

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

$\ln ({1.08}^{t}) = \ln (3)$

Step 4

Expand $\ln ({1.08}^{t})$ by moving $t$ outside the logarithm.

$t \ln (1.08) = \ln (3)$

Step 5

Divide each term in $t \ln (1.08) = \ln (3)$ by $\ln (1.08)$ and simplify.

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Step 5.1

Divide each term in $t \ln (1.08) = \ln (3)$ by $\ln (1.08)$ .

$\frac{t \ln (1.08)}{\ln (1.08)} = \frac{\ln (3)}{\ln (1.08)}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $\ln (1.08)$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{t \ln (1.08)}{\ln (1.08)} = \frac{\ln (3)}{\ln (1.08)}$

Step 5.2.1.2

Divide $t$ by $1$ .

$t = \frac{\ln (3)}{\ln (1.08)}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$t = \frac{\ln (3)}{\ln (1.08)}$

Decimal Form:

$t = 14.27491458 \dots$