 #1
chwala
Gold Member
 2,196
 285
 Homework Statement:

This is my own created problem;
Solve for ##x## given
##x^\frac{2}{3}  x^\frac{3}{2}6=0##
 Relevant Equations:
 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...
...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}16x^\frac{3}{2}=0##
##x^\frac{13}{6}6x^\frac{3}{2}1=0##
##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...
...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}16x^\frac{3}{2}=0##
##x^\frac{13}{6}6x^\frac{3}{2}1=0##
##\dfrac{13}{6}\log x1.5 \log x= \log 6##
##\dfrac{2}{3}\log x=\log6##
##\dfrac{2}{3}\log x=0.778##
##\log x=1.167##
##x=10^{1.167}=14.689## (approximate solution in my opinion)
My calculator indicates the solution as ##x=14.7617##
Your input is welcome...