Basic Math Examples

$\ln (1 - P) = - 0.0033 - 0.0051 \cdot 60$

Step 1

To solve for $P$ , rewrite the equation using properties of logarithms.

$e^{\ln (1 - P)} = e^{- 0.0033 - 0.0051 \cdot 60}$

Step 2

Rewrite $\ln (1 - P) = - 0.0033 - 0.0051 \cdot 60$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$e^{- 0.0033 - 0.0051 \cdot 60} = 1 - P$

Step 3

Solve for $P$ .

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Step 3.1

Rewrite the equation as $1 - P = e^{- 0.0033 - 0.0051 \cdot 60}$ .

$1 - P = e^{- 0.0033 - 0.0051 \cdot 60}$

Step 3.2

Simplify $e^{- 0.0033 - 0.0051 \cdot 60}$ .

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Step 3.2.1

Multiply $- 0.0051$ by $60$ .

$1 - P = e^{- 0.0033 - 0.306}$

Step 3.2.2

Subtract $0.306$ from $- 0.0033$ .

$1 - P = e^{- 0.3093}$

Step 3.2.3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$1 - P = \frac{1}{e^{0.3093}}$

Step 3.3

Subtract $1$ from both sides of the equation.

$- P = \frac{1}{e^{0.3093}} - 1$

Step 3.4

Divide each term in $- P = \frac{1}{e^{0.3093}} - 1$ by $- 1$ and simplify.

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Step 3.4.1

Divide each term in $- P = \frac{1}{e^{0.3093}} - 1$ by $- 1$ .

$\frac{- P}{- 1} = \frac{\frac{1}{e^{0.3093}}}{- 1} + \frac{- 1}{- 1}$

Step 3.4.2

Simplify the left side.

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Step 3.4.2.1

Dividing two negative values results in a positive value.

$\frac{P}{1} = \frac{\frac{1}{e^{0.3093}}}{- 1} + \frac{- 1}{- 1}$

Step 3.4.2.2

Divide $P$ by $1$ .

$P = \frac{\frac{1}{e^{0.3093}}}{- 1} + \frac{- 1}{- 1}$

Step 3.4.3

Simplify the right side.

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Step 3.4.3.1

Simplify each term.

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Step 3.4.3.1.1

Move the negative one from the denominator of $\frac{\frac{1}{e^{0.3093}}}{- 1}$ .

$P = - 1 \cdot \frac{1}{e^{0.3093}} + \frac{- 1}{- 1}$

Step 3.4.3.1.2

Rewrite $- 1 \cdot \frac{1}{e^{0.3093}}$ as $- \frac{1}{e^{0.3093}}$ .

$P = - \frac{1}{e^{0.3093}} + \frac{- 1}{- 1}$

Step 3.4.3.1.3

Divide $- 1$ by $- 1$ .

$P = - \frac{1}{e^{0.3093}} + 1$

Step 4

The result can be shown in multiple forms.

Exact Form:

$P = - \frac{1}{e^{0.3093}} + 1$

Decimal Form:

$P = 0.26603945 \dots$