Trigonometry Examples

$1680000 (1 - e^{- 0.03 x}) = 0$

Step 1

Divide each term in $1680000 (1 - e^{- 0.03 x}) = 0$ by $1680000$ and simplify.

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Step 1.1

Divide each term in $1680000 (1 - e^{- 0.03 x}) = 0$ by $1680000$ .

$\frac{1680000 (1 - e^{- 0.03 x})}{1680000} = \frac{0}{1680000}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $1680000$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{1680000 (1 - e^{- 0.03 x})}{1680000} = \frac{0}{1680000}$

Step 1.2.1.2

Divide $1 - e^{- 0.03 x}$ by $1$ .

$1 - e^{- 0.03 x} = \frac{0}{1680000}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $0$ by $1680000$ .

$1 - e^{- 0.03 x} = 0$

Step 2

Subtract $1$ from both sides of the equation.

$- e^{- 0.03 x} = - 1$

Step 3

Divide each term in $- e^{- 0.03 x} = - 1$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- e^{- 0.03 x} = - 1$ by $- 1$ .

$\frac{- e^{- 0.03 x}}{- 1} = \frac{- 1}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{e^{- 0.03 x}}{1} = \frac{- 1}{- 1}$

Step 3.2.2

Divide $e^{- 0.03 x}$ by $1$ .

$e^{- 0.03 x} = \frac{- 1}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $- 1$ by $- 1$ .

$e^{- 0.03 x} = 1$

Step 4

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

$\ln (e^{- 0.03 x}) = \ln (1)$

Step 5

Expand the left side.

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Step 5.1

Expand $\ln (e^{- 0.03 x})$ by moving $- 0.03 x$ outside the logarithm.

$- 0.03 x \ln (e) = \ln (1)$

Step 5.2

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

$- 0.03 x \cdot 1 = \ln (1)$

Step 5.3

Multiply $- 0.03$ by $1$ .

$- 0.03 x = \ln (1)$

Step 6

Simplify the right side.

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Step 6.1

The natural logarithm of $1$ is $0$ .

$- 0.03 x = 0$

Step 7

Divide each term in $- 0.03 x = 0$ by $- 0.03$ and simplify.

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Step 7.1

Divide each term in $- 0.03 x = 0$ by $- 0.03$ .

$\frac{- 0.03 x}{- 0.03} = \frac{0}{- 0.03}$

Step 7.2

Simplify the left side.

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Step 7.2.1

Cancel the common factor of $- 0.03$ .

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Step 7.2.1.1

Cancel the common factor.

$\frac{- 0.03 x}{- 0.03} = \frac{0}{- 0.03}$

Step 7.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{- 0.03}$

Step 7.3

Simplify the right side.

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Step 7.3.1

Divide $0$ by $- 0.03$ .

$x = 0$