Solve for k 1200=1200÷6.100591716*2.718281828^(-9k)

Math
1200=1200÷6.10059171⋅2.71828182-9k
Rewrite the equation as 1200÷6.10059171⋅2.71828182-9k=1200.
1200÷6.10059171⋅2.71828182-9k=1200
Divide 1200 by 6.10059171.
196.70223084⋅2.71828182-9k=1200
Divide each term by 196.70223084 and simplify.
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Divide each term in 196.70223084⋅2.71828182-9k=1200 by 196.70223084.
196.70223084⋅2.71828182-9k196.70223084=1200196.70223084
Cancel the common factor of 196.70223084.
2.71828182-9k=1200196.70223084
Divide 1200 by 196.70223084.
2.71828182-9k=6.10059171
2.71828182-9k=6.10059171
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
ln(2.71828182-9k)=ln(6.10059171)
Expand ln(2.71828182-9k) by moving -9k outside the logarithm.
-9kln(2.71828182)=ln(6.10059171)
Divide each term by -9ln(2.71828182) and simplify.
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Divide each term in -9kln(2.71828182)=ln(6.10059171) by -9ln(2.71828182).
-9kln(2.71828182)-9ln(2.71828182)=ln(6.10059171)-9ln(2.71828182)
Simplify -9kln(2.71828182)-9ln(2.71828182).
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Cancel the common factor of -9.
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Cancel the common factor.
-9kln(2.71828182)-9ln(2.71828182)=ln(6.10059171)-9ln(2.71828182)
Rewrite the expression.
kln(2.71828182)ln(2.71828182)=ln(6.10059171)-9ln(2.71828182)
kln(2.71828182)ln(2.71828182)=ln(6.10059171)-9ln(2.71828182)
Cancel the common factor of ln(2.71828182).
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Cancel the common factor.
kln(2.71828182)ln(2.71828182)=ln(6.10059171)-9ln(2.71828182)
Divide k by 1.
k=ln(6.10059171)-9ln(2.71828182)
k=ln(6.10059171)-9ln(2.71828182)
k=ln(6.10059171)-9ln(2.71828182)
Move the negative in front of the fraction.
k=-ln(6.10059171)9ln(2.71828182)
k=-ln(6.10059171)9ln(2.71828182)
The result can be shown in multiple forms.
Exact Form:
k=-ln(6.10059171)9ln(2.71828182)
Decimal Form:
k=-0.20093175…
Solve for k 1200=1200÷6.100591716*2.718281828^(-9k)

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