SOLUTION: Find the real values of x which satisfy the equation. {{{logx base3 + log3 base x =10/3 }}}

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Find the real values of x which satisfy the equation. {{{logx base3 + log3 base x =10/3 }}}      Log On


   

Question 985470: Find the real values of x which satisfy the equation.
logx+base3+%2B+log3+base+x+=10%2F3+
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
log(3,x)+log(3,x)=10/3

log%283%2Cx%29%2Blog%283%2Cx%29=10%2F3

log%283%2Cx%5E2%29=10%2F3

2%2Alog%283%2Cx%29=10%2F3

log%283%2Cx%29=5%2F3

Not sure which way you want to handle from there.
3%5E%285%2F3%29=x, fundamentally what you might want. (Exponent is five-thirds).
OR
%283%5E5%29%5E%281%2F3%29
root%283%2C3%5E5%29
highlight%283%2Aroot%283%2C3%5E2%29%29
or
highlight%283%2Aroot%283%2C9%29%29