Solve for t 1500=1000*e^(0.03t)

$1500 = 1000 \cdot e^{0.03 t}$

Rewrite the equation as $1000 \cdot e^{0.03 t} = 1500$ .

$1000 e^{0.03 t} = 1500$

Divide each term by $1000$ and simplify.

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Divide each term in $1000 e^{0.03 t} = 1500$ by $1000$ .

$\frac{1000 e^{0.03 t}}{1000} = \frac{1500}{1000}$

Cancel the common factor of $1000$ .

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Cancel the common factor.

$\frac{1000 e^{0.03 t}}{1000} = \frac{1500}{1000}$

Divide $e^{0.03 t}$ by $1$ .

$e^{0.03 t} = \frac{1500}{1000}$

Cancel the common factor of $1500$ and $1000$ .

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Factor $500$ out of $1500$ .

$e^{0.03 t} = \frac{500 (3)}{1000}$

Cancel the common factors.

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Factor $500$ out of $1000$ .

$e^{0.03 t} = \frac{500 \cdot 3}{500 \cdot 2}$

Cancel the common factor.

$e^{0.03 t} = \frac{500 \cdot 3}{500 \cdot 2}$

Rewrite the expression.

$e^{0.03 t} = \frac{3}{2}$

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

$\ln (e^{0.03 t}) = \ln (\frac{3}{2})$

Use logarithm rules to move $0.03 t$ out of the exponent.

$0.03 t \ln (e) = \ln (\frac{3}{2})$

The natural logarithm of $e$ is $1$ .

$0.03 t \cdot 1 = \ln (\frac{3}{2})$

Multiply $0.03$ by $1$ .

$0.03 t = \ln (\frac{3}{2})$

Divide each term by $0.03$ and simplify.

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Divide each term in $0.03 t = \ln (\frac{3}{2})$ by $0.03$ .

$\frac{0.03 t}{0.03} = \frac{\ln (\frac{3}{2})}{0.03}$

Cancel the common factor of $0.03$ .

$t = \frac{\ln (\frac{3}{2})}{0.03}$

Simplify $\frac{\ln (\frac{3}{2})}{0.03}$ .

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Multiply by $1$ .

$t = \frac{1 \ln (\frac{3}{2})}{0.03}$

Factor $0.03$ out of $0.03$ .

$t = \frac{1 \ln (\frac{3}{2})}{0.03 (1)}$

Separate fractions.

$t = \frac{1}{0.03} \cdot \frac{\ln (\frac{3}{2})}{1}$

Divide $1$ by $0.03$ .

$t = 33.\overline{3} (\frac{\ln (\frac{3}{2})}{1})$

Divide $\ln (\frac{3}{2})$ by $1$ .

$t = 33.\overline{3} \ln (\frac{3}{2})$

Multiply $33.\overline{3}$ by $\ln (\frac{3}{2})$ .

$t = 13.5155036$

Solve for t 1500=1000*e^(0.03t)

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