Basic Math Examples

$\frac{1534}{1142} = e^{2 k}$

Step 1

Rewrite the equation as $e^{2 k} = \frac{1534}{1142}$ .

$e^{2 k} = \frac{1534}{1142}$

Step 2

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

$\ln (e^{2 k}) = \ln (\frac{1534}{1142})$

Step 3

Expand the left side.

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Step 3.1

Expand $\ln (e^{2 k})$ by moving $2 k$ outside the logarithm.

$2 k \ln (e) = \ln (\frac{1534}{1142})$

Step 3.2

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

$2 k \cdot 1 = \ln (\frac{1534}{1142})$

Step 3.3

Multiply $2$ by $1$ .

$2 k = \ln (\frac{1534}{1142})$

Step 4

Simplify the right side.

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Step 4.1

Cancel the common factor of $1534$ and $1142$ .

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Step 4.1.1

Factor $2$ out of $1534$ .

$2 k = \ln (\frac{2 (767)}{1142})$

Step 4.1.2

Cancel the common factors.

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Step 4.1.2.1

Factor $2$ out of $1142$ .

$2 k = \ln (\frac{2 \cdot 767}{2 \cdot 571})$

Step 4.1.2.2

Cancel the common factor.

$2 k = \ln (\frac{2 \cdot 767}{2 \cdot 571})$

Step 4.1.2.3

Rewrite the expression.

$2 k = \ln (\frac{767}{571})$

Step 5

Divide each term in $2 k = \ln (\frac{767}{571})$ by $2$ and simplify.

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Step 5.1

Divide each term in $2 k = \ln (\frac{767}{571})$ by $2$ .

$\frac{2 k}{2} = \frac{\ln (\frac{767}{571})}{2}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $2$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{2 k}{2} = \frac{\ln (\frac{767}{571})}{2}$

Step 5.2.1.2

Divide $k$ by $1$ .

$k = \frac{\ln (\frac{767}{571})}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$k = \frac{\ln (\frac{767}{571})}{2}$

Decimal Form:

$k = 0.14754879 \dots$