Precalculus Examples

$25 e^{x} = 1000$

Step 1

Divide each term in $25 e^{x} = 1000$ by $25$ and simplify.

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Step 1.1

Divide each term in $25 e^{x} = 1000$ by $25$ .

$\frac{25 e^{x}}{25} = \frac{1000}{25}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $25$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{25 e^{x}}{25} = \frac{1000}{25}$

Step 1.2.1.2

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

$e^{x} = \frac{1000}{25}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $1000$ by $25$ .

$e^{x} = 40$

Step 2

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

$\ln (e^{x}) = \ln (40)$

Step 3

Expand the left side.

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Step 3.1

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

$x \ln (e) = \ln (40)$

Step 3.2

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

$x \cdot 1 = \ln (40)$

Step 3.3

Multiply $x$ by $1$ .

$x = \ln (40)$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \ln (40)$

Decimal Form:

$x = 3.68887945 \dots$