# Solve for k 9790=271.82^(7k) 9790=271.827k
Rewrite the equation as 271.827k=9790.
271.827k=9790
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
ln(271.827k)=ln(9790)
Expand ln(271.827k) by moving 7k outside the logarithm.
7kln(271.82)=ln(9790)
Divide each term by 7ln(271.82) and simplify.
Divide each term in 7kln(271.82)=ln(9790) by 7ln(271.82).
7kln(271.82)7ln(271.82)=ln(9790)7ln(271.82)
Simplify 7kln(271.82)7ln(271.82).
Cancel the common factor of 7.
Cancel the common factor.
7kln(271.82)7ln(271.82)=ln(9790)7ln(271.82)
Rewrite the expression.
kln(271.82)ln(271.82)=ln(9790)7ln(271.82)
kln(271.82)ln(271.82)=ln(9790)7ln(271.82)
Cancel the common factor of ln(271.82).
Cancel the common factor.
kln(271.82)ln(271.82)=ln(9790)7ln(271.82)
Divide k by 1.
k=ln(9790)7ln(271.82)
k=ln(9790)7ln(271.82)
k=ln(9790)7ln(271.82)
k=ln(9790)7ln(271.82)
The result can be shown in multiple forms.
Exact Form:
k=ln(9790)7ln(271.82)
Decimal Form:
k=0.23420127…
Solve for k 9790=271.82^(7k)

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