Algebra Examples

$\frac{- 1}{k} \ln (\frac{P}{14.7}) = A$

Step 1

Simplify $\frac{- 1}{k} \cdot \ln (\frac{P}{14.7})$ .

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Step 1.1

Move the negative in front of the fraction.

$- \frac{1}{k} \cdot \ln (\frac{P}{14.7}) = A$

Step 1.2

Multiply by $1$ .

$- \frac{1}{k} \cdot \ln (\frac{1 P}{14.7}) = A$

Step 1.3

Factor $14.7$ out of $14.7$ .

$- \frac{1}{k} \cdot \ln (\frac{1 P}{14.7 (1)}) = A$

Step 1.4

Separate fractions.

$- \frac{1}{k} \cdot \ln (\frac{1}{14.7} \cdot \frac{P}{1}) = A$

Step 1.5

Simplify the expression.

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Step 1.5.1

Divide $1$ by $14.7$ .

$- \frac{1}{k} \cdot \ln (0.06802721 \frac{P}{1}) = A$

Step 1.5.2

Divide $P$ by $1$ .

$- \frac{1}{k} \cdot \ln (0.06802721 P) = A$

Step 1.6

Combine $\ln (0.06802721 P)$ and $\frac{1}{k}$ .

$- \frac{\ln (0.06802721 P)}{k} = A$

Step 2

Divide each term in $- \frac{\ln (0.06802721 P)}{k} = A$ by $- 1$ and simplify.

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Step 2.1

Divide each term in $- \frac{\ln (0.06802721 P)}{k} = A$ by $- 1$ .

$\frac{- \frac{\ln (0.06802721 P)}{k}}{- 1} = \frac{A}{- 1}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

$\frac{\frac{\ln (0.06802721 P)}{k}}{1} = \frac{A}{- 1}$

Step 2.2.2

Divide $\frac{\ln (0.06802721 P)}{k}$ by $1$ .

$\frac{\ln (0.06802721 P)}{k} = \frac{A}{- 1}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Move the negative one from the denominator of $\frac{A}{- 1}$ .

$\frac{\ln (0.06802721 P)}{k} = - 1 \cdot A$

Step 2.3.2

Rewrite $- 1 \cdot A$ as $- A$ .

$\frac{\ln (0.06802721 P)}{k} = - A$

Step 3

Multiply both sides by $k$ .

$\frac{\ln (0.06802721 P)}{k} k = - A k$

Step 4

Simplify the left side.

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Step 4.1

Cancel the common factor of $k$ .

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Step 4.1.1

Cancel the common factor.

$\frac{\ln (0.06802721 P)}{k} k = - A k$

Step 4.1.2

Rewrite the expression.

$\ln (0.06802721 P) = - A k$

Step 5

Solve for $P$ .

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Step 5.1

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

$e^{\ln (0.06802721 P)} = e^{- A k}$

Step 5.2

Rewrite $\ln (0.06802721 P) = - A k$ 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 $b^{y} = x$ .

$e^{- A k} = 0.06802721 P$

Step 5.3

Solve for $P$ .

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Step 5.3.1

Rewrite the equation as $0.06802721 P = e^{- A k}$ .

$0.06802721 P = e^{- A k}$

Step 5.3.2

Divide each term in $0.06802721 P = e^{- A k}$ by $0.06802721$ and simplify.

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Step 5.3.2.1

Divide each term in $0.06802721 P = e^{- A k}$ by $0.06802721$ .

$\frac{0.06802721 P}{0.06802721} = \frac{e^{- A k}}{0.06802721}$

Step 5.3.2.2

Simplify the left side.

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Step 5.3.2.2.1

Cancel the common factor of $0.06802721$ .

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Step 5.3.2.2.1.1

Cancel the common factor.

$\frac{0.06802721 P}{0.06802721} = \frac{e^{- A k}}{0.06802721}$

Step 5.3.2.2.1.2

Divide $P$ by $1$ .

$P = \frac{e^{- A k}}{0.06802721}$

Step 5.3.2.3

Simplify the right side.

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Step 5.3.2.3.1

Multiply by $1$ .

$P = \frac{1 e^{- A k}}{0.06802721}$

Step 5.3.2.3.2

Factor $0.06802721$ out of $0.06802721$ .

$P = \frac{1 e^{- A k}}{0.06802721 (1)}$

Step 5.3.2.3.3

Separate fractions.

$P = \frac{1}{0.06802721} \cdot \frac{e^{- A k}}{1}$

Step 5.3.2.3.4

Divide $1$ by $0.06802721$ .

$P = 14.6\overline{9} \frac{e^{- A k}}{1}$

Step 5.3.2.3.5

Divide $e^{- A k}$ by $1$ .

$P = 14.6\overline{9} e^{- A k}$