# Solve for r 20024=13800^((r)(6))

20024=13800(r)(6)
Rewrite the equation as 13800(r)(6)=20024.
13800(r)(6)=20024
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
ln(13800(r)(6))=ln(20024)
Expand ln(13800(r)(6)) by moving (r)(6) outside the logarithm.
(r)(6)ln(13800)=ln(20024)
Move 6 to the left of r.
6rln(13800)=ln(20024)
Divide each term by 6ln(13800) and simplify.
Divide each term in 6rln(13800)=ln(20024) by 6ln(13800).
6rln(13800)6ln(13800)=ln(20024)6ln(13800)
Simplify 6rln(13800)6ln(13800).
Cancel the common factor of 6.
Cancel the common factor.
6rln(13800)6ln(13800)=ln(20024)6ln(13800)
Rewrite the expression.
rln(13800)ln(13800)=ln(20024)6ln(13800)
rln(13800)ln(13800)=ln(20024)6ln(13800)
Cancel the common factor of ln(13800).
Cancel the common factor.
rln(13800)ln(13800)=ln(20024)6ln(13800)
Divide r by 1.
r=ln(20024)6ln(13800)
r=ln(20024)6ln(13800)
r=ln(20024)6ln(13800)
r=ln(20024)6ln(13800)
The result can be shown in multiple forms.
Exact Form:
r=ln(20024)6ln(13800)
Decimal Form:
r=0.17317538…
Solve for r 20024=13800^((r)(6))

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