Solve for k natural log of k/A=(-E)/(RT)

$\ln (\frac{k}{A}) = \frac{- E}{R T}$

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

$e^{\ln (\frac{k}{A})} = e^{\frac{- E}{R T}}$

Rewrite $\ln (\frac{k}{A}) = \frac{- E}{R T}$ 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 $b^{y} = x$ .

$e^{\frac{- E}{R T}} = \frac{k}{A}$

Solve for $k$ .

Rewrite the equation as $\frac{k}{A} = e^{\frac{- E}{R T}}$ .

$\frac{k}{A} = e^{\frac{- E}{R T}}$

Multiply both sides by $A$ .

$\frac{k}{A} A = e^{\frac{- E}{R T}} A$

Simplify.

Simplify the left side.

Cancel the common factor of $A$ .

Cancel the common factor.

$\frac{k}{A} A = e^{\frac{- E}{R T}} A$

Rewrite the expression.

$k = e^{\frac{- E}{R T}} A$

Simplify the right side.

Simplify $e^{\frac{- E}{R T}} A$ .

Move the negative in front of the fraction.

$k = e^{- \frac{E}{R T}} A$

Reorder factors in $e^{- \frac{E}{R T}} A$ .

$k = A e^{- \frac{E}{R T}}$

Solve for k natural log of k/A=(-E)/(RT)

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