Finite Math Examples

$4 p = e^{0.84 t}$

Step 1

Rewrite the equation as $e^{0.84 t} = 4 p$ .

$e^{0.84 t} = 4 p$

Step 2

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

$\ln (e^{0.84 t}) = \ln (4 p)$

Step 3

Expand the left side.

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Step 3.1

Expand $\ln (e^{0.84 t})$ by moving $0.84 t$ outside the logarithm.

$0.84 t \ln (e) = \ln (4 p)$

Step 3.2

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

$0.84 t \cdot 1 = \ln (4 p)$

Step 3.3

Multiply $0.84$ by $1$ .

$0.84 t = \ln (4 p)$

Step 4

Divide each term in $0.84 t = \ln (4 p)$ by $0.84$ and simplify.

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Step 4.1

Divide each term in $0.84 t = \ln (4 p)$ by $0.84$ .

$\frac{0.84 t}{0.84} = \frac{\ln (4 p)}{0.84}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $0.84$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{0.84 t}{0.84} = \frac{\ln (4 p)}{0.84}$

Step 4.2.1.2

Divide $t$ by $1$ .

$t = \frac{\ln (4 p)}{0.84}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Multiply by $1$ .

$t = \frac{1 \ln (4 p)}{0.84}$

Step 4.3.2

Factor $0.84$ out of $0.84$ .

$t = \frac{1 \ln (4 p)}{0.84 (1)}$

Step 4.3.3

Separate fractions.

$t = \frac{1}{0.84} \cdot \frac{\ln (4 p)}{1}$

Step 4.3.4

Divide $1$ by $0.84$ .

$t = 1.\overline{190476} \frac{\ln (4 p)}{1}$

Step 4.3.5

Divide $\ln (4 p)$ by $1$ .

$t = 1.\overline{190476} \ln (4 p)$