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Precalculus Mathematics Homework Help
Solve the given equation that involves fractional indices
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[QUOTE="chwala, post: 6848070, member: 287397"] [B]Homework Statement:[/B] This is my own created problem; Solve for ##x## given ##x^\frac{2}{3} - x^\frac{-3}{2}-6=0## [B]Relevant Equations:[/B] understanding of indices The actual problem that i was looking at with my students was supposed to be ##x^\frac{2}{3} - x^\frac{-2}{3}-6=0##(which is easy to solve using quadratic equations) of which i wanted them to solve, ...then i realized then that i had erronously posted ##x^\frac{2}{3} - x^\frac{-3}{2}-6=0## on the board...and they were not able to proceed... :cool: ...anyway, i want to see if we can solve the problem as it is...##x^\frac{2}{3} - x^\frac{-3}{2}-6=0## My take; ##x^\frac{2}{3}⋅x^\frac{3}{2}-1-6x^\frac{3}{2}=0## ##x^\frac{13}{6}-6x^\frac{3}{2}-1=0## [INDENT]##\dfrac{13}{6}\log x-1.5 \log x= \log 6##[/INDENT] [INDENT][/INDENT] [INDENT]##\dfrac{2}{3}\log x=\log6##[/INDENT] [INDENT][/INDENT] [INDENT]##\dfrac{2}{3}\log x=0.778##[/INDENT] [INDENT][/INDENT] [INDENT]##\log x=1.167##[/INDENT] [INDENT][/INDENT] [INDENT]##x=10^{1.167}=14.689## (approximate solution in my opinion)[/INDENT] [INDENT][/INDENT] [INDENT]My calculator indicates the solution as ##x=14.7617##[/INDENT] [INDENT][/INDENT] [INDENT]Your input is welcome...[/INDENT] [/QUOTE]
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Precalculus Mathematics Homework Help
Solve the given equation that involves fractional indices
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