Solve for k 2=e^(58k)

$2 = e^{58 k}$

Step 1

Rewrite the equation as $e^{58 k} = 2$ .

$e^{58 k} = 2$

Step 2

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

$\ln (e^{58 k}) = \ln (2)$

Step 3

Expand the left side.

Expand $\ln (e^{58 k})$ by moving $58 k$ outside the logarithm.

$58 k \ln (e) = \ln (2)$

The natural logarithm of $e$ is $1$ .

$58 k \cdot 1 = \ln (2)$

Multiply $58$ by $1$ .

$58 k = \ln (2)$

Step 4

Divide each term in $58 k = \ln (2)$ by $58$ and simplify.

Divide each term in $58 k = \ln (2)$ by $58$ .

$\frac{58 k}{58} = \frac{\ln (2)}{58}$

Simplify the left side.

Cancel the common factor of $58$ .

Cancel the common factor.

$\frac{58 k}{58} = \frac{\ln (2)}{58}$

Divide $k$ by $1$ .

$k = \frac{\ln (2)}{58}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$k = \frac{\ln (2)}{58}$

Decimal Form:

$k = 0.01195081 \dots$