Precalculus Examples

$150 = 50 e^{7 x}$

Step 1

Rewrite the equation as $50 e^{7 x} = 150$ .

$50 e^{7 x} = 150$

Step 2

Divide each term in $50 e^{7 x} = 150$ by $50$ and simplify.

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Step 2.1

Divide each term in $50 e^{7 x} = 150$ by $50$ .

$\frac{50 e^{7 x}}{50} = \frac{150}{50}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $50$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{50 e^{7 x}}{50} = \frac{150}{50}$

Step 2.2.1.2

Divide $e^{7 x}$ by $1$ .

$e^{7 x} = \frac{150}{50}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $150$ by $50$ .

$e^{7 x} = 3$

Step 3

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

$\ln (e^{7 x}) = \ln (3)$

Step 4

Expand the left side.

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Step 4.1

Expand $\ln (e^{7 x})$ by moving $7 x$ outside the logarithm.

$7 x \ln (e) = \ln (3)$

Step 4.2

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

$7 x \cdot 1 = \ln (3)$

Step 4.3

Multiply $7$ by $1$ .

$7 x = \ln (3)$

Step 5

Divide each term in $7 x = \ln (3)$ by $7$ and simplify.

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Step 5.1

Divide each term in $7 x = \ln (3)$ by $7$ .

$\frac{7 x}{7} = \frac{\ln (3)}{7}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $7$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{\ln (3)}{7}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (3)}{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (3)}{7}$

Decimal Form:

$x = 0.15694461 \dots$