Basic Math Examples

$1200 = 1200 \div 6.10059171 \cdot {2.71828182}^{- 9 k}$

Step 1

Rewrite the equation as $1200 \div 6.10059171 \cdot {2.71828182}^{- 9 k} = 1200$ .

$1200 \div 6.10059171 \cdot {2.71828182}^{- 9 k} = 1200$

Step 2

Divide $1200$ by $6.10059171$ .

$196.70223084 \cdot {2.71828182}^{- 9 k} = 1200$

Step 3

Divide each term in $196.70223084 \cdot {2.71828182}^{- 9 k} = 1200$ by $196.70223084$ and simplify.

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Step 3.1

Divide each term in $196.70223084 \cdot {2.71828182}^{- 9 k} = 1200$ by $196.70223084$ .

$\frac{196.70223084 \cdot {2.71828182}^{- 9 k}}{196.70223084} = \frac{1200}{196.70223084}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $196.70223084$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{196.70223084 \cdot {2.71828182}^{- 9 k}}{196.70223084} = \frac{1200}{196.70223084}$

Step 3.2.1.2

Divide ${2.71828182}^{- 9 k}$ by $1$ .

${2.71828182}^{- 9 k} = \frac{1200}{196.70223084}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $1200$ by $196.70223084$ .

${2.71828182}^{- 9 k} = 6.10059171$

Step 4

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

$\ln ({2.71828182}^{- 9 k}) = \ln (6.10059171)$

Step 5

Expand $\ln ({2.71828182}^{- 9 k})$ by moving $- 9 k$ outside the logarithm.

$- 9 k \ln (2.71828182) = \ln (6.10059171)$

Step 6

Divide each term in $- 9 k \ln (2.71828182) = \ln (6.10059171)$ by $- 9 \ln (2.71828182)$ and simplify.

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Step 6.1

Divide each term in $- 9 k \ln (2.71828182) = \ln (6.10059171)$ by $- 9 \ln (2.71828182)$ .

$\frac{- 9 k \ln (2.71828182)}{- 9 \ln (2.71828182)} = \frac{\ln (6.10059171)}{- 9 \ln (2.71828182)}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $- 9$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{- 9 k \ln (2.71828182)}{- 9 \ln (2.71828182)} = \frac{\ln (6.10059171)}{- 9 \ln (2.71828182)}$

Step 6.2.1.2

Rewrite the expression.

$\frac{k \ln (2.71828182)}{\ln (2.71828182)} = \frac{\ln (6.10059171)}{- 9 \ln (2.71828182)}$

Step 6.2.2

Cancel the common factor of $\ln (2.71828182)$ .

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Step 6.2.2.1

Cancel the common factor.

$\frac{k \ln (2.71828182)}{\ln (2.71828182)} = \frac{\ln (6.10059171)}{- 9 \ln (2.71828182)}$

Step 6.2.2.2

Divide $k$ by $1$ .

$k = \frac{\ln (6.10059171)}{- 9 \ln (2.71828182)}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Move the negative in front of the fraction.

$k = - \frac{\ln (6.10059171)}{9 \ln (2.71828182)}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$k = - \frac{\ln (6.10059171)}{9 \ln (2.71828182)}$

Decimal Form:

$k = - 0.20093175 \dots$