Calculus Examples

e^{0.06 x} = 3

$e^{0.06 x} = 3$

Step 1

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

\ln (e^{0.06 x}) = \ln (3)

$\ln (e^{0.06 x}) = \ln (3)$

Step 2

Expand the left side.

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Step 2.1

Expand

\ln (e^{0.06 x})

$\ln (e^{0.06 x})$ by moving

0.06 x

$0.06 x$ outside the logarithm.

0.06 x \ln (e) = \ln (3)

$0.06 x \ln (e) = \ln (3)$

Step 2.2

The natural logarithm of

e

$e$ is

1

$1$ .

0.06 x \cdot 1 = \ln (3)

$0.06 x \cdot 1 = \ln (3)$

Step 2.3

Multiply

0.06

$0.06$ by

1

$1$ .

0.06 x = \ln (3)

$0.06 x = \ln (3)$

0.06 x = \ln (3)

$0.06 x = \ln (3)$

Step 3

Divide each term in

0.06 x = \ln (3)

$0.06 x = \ln (3)$ by

0.06

$0.06$ and simplify.

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Step 3.1

Divide each term in

0.06 x = \ln (3)

$0.06 x = \ln (3)$ by

0.06

$0.06$ .

\frac{0.06 x}{0.06} = \frac{\ln (3)}{0.06}

$\frac{0.06 x}{0.06} = \frac{\ln (3)}{0.06}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of

0.06

$0.06$ .

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Step 3.2.1.1

Cancel the common factor.

\frac{0.06 x}{0.06} = \frac{\ln (3)}{0.06}

$\frac{0.06 x}{0.06} = \frac{\ln (3)}{0.06}$

Step 3.2.1.2

Divide

x

$x$ by

1

$1$ .

x = \frac{\ln (3)}{0.06}

$x = \frac{\ln (3)}{0.06}$

x = \frac{\ln (3)}{0.06}

$x = \frac{\ln (3)}{0.06}$

x = \frac{\ln (3)}{0.06}

$x = \frac{\ln (3)}{0.06}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Replace

e

$e$ with an approximation.

x = \frac{\log_{2.71828182} (3)}{0.06}

$x = \frac{\log_{2.71828182} (3)}{0.06}$

Step 3.3.2

Log base

2.71828182

$2.71828182$ of

3

$3$ is approximately

1.09861228

$1.09861228$ .

x = \frac{1.09861228}{0.06}

$x = \frac{1.09861228}{0.06}$

Step 3.3.3

Divide

1.09861228

$1.09861228$ by

0.06

$0.06$ .

x = 18.31020481

$x = 18.31020481$

x = 18.31020481

$x = 18.31020481$

x = 18.31020481

$x = 18.31020481$

e^{0.06 x} = 3

$e^{0.06 x} = 3$

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[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$