Calculus Examples

$p = 300 e^{- 0.3 q}$

Step 1

Rewrite the equation as $300 e^{- 0.3 q} = p$ .

$300 e^{- 0.3 q} = p$

Step 2

Divide each term in $300 e^{- 0.3 q} = p$ by $300$ and simplify.

Tap for more steps...

Step 2.1

Divide each term in $300 e^{- 0.3 q} = p$ by $300$ .

$\frac{300 e^{- 0.3 q}}{300} = \frac{p}{300}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $300$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{300 e^{- 0.3 q}}{300} = \frac{p}{300}$

Step 2.2.1.2

Divide $e^{- 0.3 q}$ by $1$ .

$e^{- 0.3 q} = \frac{p}{300}$

Step 3

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

$\ln (e^{- 0.3 q}) = \ln (\frac{p}{300})$

Step 4

Expand the left side.

Tap for more steps...

Step 4.1

Expand $\ln (e^{- 0.3 q})$ by moving $- 0.3 q$ outside the logarithm.

$- 0.3 q \ln (e) = \ln (\frac{p}{300})$

Step 4.2

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

$- 0.3 q \cdot 1 = \ln (\frac{p}{300})$

Step 4.3

Multiply $- 0.3$ by $1$ .

$- 0.3 q = \ln (\frac{p}{300})$

Step 5

Divide each term in $- 0.3 q = \ln (\frac{p}{300})$ by $- 0.3$ and simplify.

Tap for more steps...

Step 5.1

Divide each term in $- 0.3 q = \ln (\frac{p}{300})$ by $- 0.3$ .

$\frac{- 0.3 q}{- 0.3} = \frac{\ln (\frac{p}{300})}{- 0.3}$

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Cancel the common factor of $- 0.3$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor.

$\frac{- 0.3 q}{- 0.3} = \frac{\ln (\frac{p}{300})}{- 0.3}$

Step 5.2.1.2

Divide $q$ by $1$ .

$q = \frac{\ln (\frac{p}{300})}{- 0.3}$

Step 5.3

Simplify the right side.

Tap for more steps...

Step 5.3.1

Move the negative in front of the fraction.

$q = - \frac{\ln (\frac{p}{300})}{0.3}$

Step 5.3.2

Multiply by $1$ .

$q = - \frac{1 \ln (\frac{p}{300})}{0.3}$

Step 5.3.3

Factor $0.3$ out of $0.3$ .

$q = - \frac{1 \ln (\frac{p}{300})}{0.3 (1)}$

Step 5.3.4

Separate fractions.

$q = - (\frac{1}{0.3} \cdot \frac{\ln (\frac{p}{300})}{1})$

Step 5.3.5

Divide $1$ by $0.3$ .

$q = - (3.\overline{3} \frac{\ln (\frac{p}{300})}{1})$

Step 5.3.6

Divide $\ln (\frac{p}{300})$ by $1$ .

$q = - (3.\overline{3} \ln (\frac{p}{300}))$

Step 5.3.7

Multiply $3.\overline{3}$ by $- 1$ .

$q = - 3.\overline{3} \ln (\frac{p}{300})$