SOLUTION: Find the real values of x which satisfy the equation. Log[base3]x+log[basex]3=10/3

Algebra.Com
Question 985654: Find the real values of x which satisfy the equation.
Log[base3]x+log[basex]3=10/3
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
Log[base3]x+log[basex]3=10/3


Use the base-swapping formula 
on the second term on the left:



Let u = log3(x)



Multiply through by LCD = 3u

      3uČ + 3 = 10u

3uČ - 10u + 3 = 0

  (u-3)(3u-1) = 0

u-3=0;  3u-1=0
  u=3;    3u=1
           u=

Substitute u = log3(x)

log3(x) = 3;   log3(x) = 

  x = 33       x = 
                   
  x = 27        x = 

Edwin
RELATED QUESTIONS

Find the real values of x which satisfy the equation.... (answered by josgarithmetic)
Find the real values of x which satisfy the equation. {{{logx base3 +... (answered by josgarithmetic)
express as a logarithm of a single number: 1. log basex 20 + logbasex 2 2. 3 log... (answered by lwsshak3)
Use properties of logarithms to solve the equation log(base3)x + log(base3)(x + 2) =... (answered by ankor@dixie-net.com)
solve the equation. log(base... (answered by lwsshak3)
log base3 (x+2)+log... (answered by ankor@dixie-net.com)
log(6x-3)base... (answered by harpazo)
Find the value of 1 + 2^sqrt log 3base2 - 3^sqrt log 2... (answered by lwsshak3)
Solve the equation 3log[base5]x - log[base5]4 = log[base5]16. Solve the equation... (answered by drk)