Trigonometry Examples

$\ln (\frac{13}{6.34}) = \ln (e^{k \cdot 77})$

Step 1

Since $k$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$\ln (e^{k \cdot 77}) = \ln (\frac{13}{6.34})$

Step 2

Expand $\ln (e^{k \cdot 77})$ .

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Step 2.1

Expand $\ln (e^{k \cdot 77})$ by moving $k \cdot 77$ outside the logarithm.

$k \cdot 77 \ln (e)$

Step 2.2

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

$k \cdot 77 \cdot 1$

Step 2.3

Multiply $k$ by $1$ .

$77 \cdot k$

Step 3

The expanded equation is $77 \cdot k = \ln (\frac{13}{6.34})$ .

$77 \cdot k = \ln (\frac{13}{6.34})$

Step 4

Divide $13$ by $6.34$ .

$77 \cdot k = \ln (2.05047318)$

Step 5

Divide each term in $77 \cdot k = \ln (2.05047318)$ by $77$ and simplify.

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Step 5.1

Divide each term in $77 \cdot k = \ln (2.05047318)$ by $77$ .

$\frac{77 \cdot k}{77} = \frac{\ln (2.05047318)}{77}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $77$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{77 \cdot k}{77} = \frac{\ln (2.05047318)}{77}$

Step 5.2.1.2

Divide $k$ by $1$ .

$k = \frac{\ln (2.05047318)}{77}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$k = \frac{\ln (2.05047318)}{77}$

Decimal Form:

$k = 0.00932559 \dots$