SOLUTION: Find the real values of x which satisfy the equation. {{{log(x,3)+log(3,x)=10/3}}}

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Find the real values of x which satisfy the equation. {{{log(x,3)+log(3,x)=10/3}}}      Log On


   

Question 985655: Find the real values of x which satisfy the equation.
log%28x%2C3%29%2Blog%283%2Cx%29=10%2F3
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
log%28x%2C3%29%2Blog%283%2Cx%29=10%2F3
log%283%2C3%29%2Flog%283%2Cx%29%2Blog%283%2Cx%29=10%2F3
log%283%2C3%29%2Blog%283%2Cx%29log%283%2Cx%29=%2810%2F3%29log%283%2Cx%29
3%2A%28log%283%2Cx%29%29%5E2-10%2Alog%283%2Cx%29%2B3=0
which is in quadratic form, and you can use general solution formula for quadratic equation.

log%283%2Cx%29=%2810%2B-+sqrt%28100-4%2A3%2A3%29%29%2F6

log%283%2Cx%29=1%2F3 OR log%283%2Cx%29=3
Simple from here; otherwise say if still some trouble.