Solve for P -1/k natural log of P/14.7=A

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

Combine $\frac{- 1}{k}$ and $\ln (\frac{P}{14.7})$ .

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

Multiply each term in $\frac{- \ln (\frac{P}{14.7})}{k} = A$ by $\frac{k}{- 1}$ to eliminate the fractions.

Multiply each term in $\frac{- \ln (\frac{P}{14.7})}{k} = A$ by $\frac{k}{- 1}$ .

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

Simplify the left side.

Cancel the common factor of $k$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify $\frac{1}{- 1} \ln (\frac{P}{14.7})$ by moving $- \frac{1}{- 1}$ inside the logarithm.

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

Multiply $- 1$ by $- 1$ .

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

Multiply $\ln ({(\frac{P}{14.7})}^{- \frac{1}{- 1}})$ by $1$ .

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

Multiply by $1$ .

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

Factor $14.7$ out of $14.7$ .

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

Separate fractions.

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

Divide $1$ by $14.7$ .

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

Divide $P$ by $1$ .

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

Divide $1$ by $- 1$ .

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

Multiply $- 1$ by $- 1$ .

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

Simplify.

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

Simplify the right side.

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

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

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

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

Rewrite using the commutative property of multiplication.

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

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

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

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 $b^{y} = x$ .

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

Solve for $P$ .

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

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

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

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

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

Simplify the left side.

Cancel the common factor of $0.06802721$ .

Cancel the common factor.

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

Divide $P$ by $1$ .

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

Simplify the right side.

Multiply by $1$ .

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

Factor $0.06802721$ out of $0.06802721$ .

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

Separate fractions.

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

Divide $1$ by $0.06802721$ .

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

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

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

Solve for P -1/k natural log of P/14.7=A

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