Calculus Examples

$A (3) = 1000 e^{(\ln (1.4)) (3)}$

Step 1

Simplify.

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Step 1.1

Move $3$ to the left of $\ln (1.4)$ .

$A (3) = 1000 e^{3 \cdot \ln (1.4)}$

Step 1.2

Simplify $3 \ln (1.4)$ by moving $3$ inside the logarithm.

$A (3) = 1000 e^{\ln ({1.4}^{3})}$

Step 1.3

Exponentiation and log are inverse functions.

$A (3) = 1000 \cdot {1.4}^{3}$

Step 1.4

Raise $1.4$ to the power of $3$ .

$A (3) = 1000 \cdot 2.744$

Step 1.5

Multiply $1000$ by $2.744$ .

$A (3) = 2744$

$A (3) = 2744$

Step 2

Divide each term in $A (3) = 2744$ by $3$ and simplify.

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Step 2.1

Divide each term in $A (3) = 2744$ by $3$ .

$\frac{A (3)}{3} = \frac{2744}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{A \cdot 3}{3} = \frac{2744}{3}$

Step 2.2.1.2

Divide $A$ by $1$ .

$A = \frac{2744}{3}$

$A = \frac{2744}{3}$

$A = \frac{2744}{3}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $2744$ and $3$ .

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Step 2.3.1.1

Rewrite $2744$ as $1 (2744)$ .

$A = \frac{1 (2744)}{3}$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Rewrite $3$ as $1 (3)$ .

$A = \frac{1 \cdot 2744}{1 \cdot 3}$

Step 2.3.1.2.2

Cancel the common factor.

$A = \frac{1 \cdot 2744}{1 \cdot 3}$

Step 2.3.1.2.3

Rewrite the expression.

$A = \frac{2744}{3}$

$A = \frac{2744}{3}$

$A = \frac{2744}{3}$

$A = \frac{2744}{3}$

$A = \frac{2744}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$A = \frac{2744}{3}$

Decimal Form:

$A = 914.\overline{6}$

Mixed Number Form:

$A = 914 \frac{2}{3}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$