Calculus Examples

$9 - 2 e^{x} = 7$

Step 1

Move all terms not containing $x$ to the right side of the equation.

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Step 1.1

Subtract $9$ from both sides of the equation.

$- 2 e^{x} = 7 - 9$

Step 1.2

Subtract $9$ from $7$ .

$- 2 e^{x} = - 2$

Step 2

Divide each term in $- 2 e^{x} = - 2$ by $- 2$ and simplify.

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Step 2.1

Divide each term in $- 2 e^{x} = - 2$ by $- 2$ .

$\frac{- 2 e^{x}}{- 2} = \frac{- 2}{- 2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 2 e^{x}}{- 2} = \frac{- 2}{- 2}$

Step 2.2.1.2

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

$e^{x} = \frac{- 2}{- 2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $- 2$ by $- 2$ .

$e^{x} = 1$

Step 3

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

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

Step 4

Expand the left side.

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

Multiply $x$ by $1$ .

$x = \ln (1)$

Step 5

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

$x = 0$