SOLUTION: I am trying to figure out how to simplify and hence solve the following equation. {{{log(x, 5) + log(5, x) = 2}}} I know {{{log(b, x)=1/log(x, b)}}} but I am stuck as I don't k

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I am trying to figure out how to simplify and hence solve the following equation. {{{log(x, 5) + log(5, x) = 2}}} I know {{{log(b, x)=1/log(x, b)}}} but I am stuck as I don't k      Log On


   

Question 11901: I am trying to figure out how to simplify and hence solve the following equation.
log%28x%2C+5%29+%2B+log%285%2C+x%29+=+2
I know log%28b%2C+x%29=1%2Flog%28x%2C+b%29 but I am stuck as I don't know how to deal with 1%2Flog%28x%2C+5%29 other than to make it %28log%28x%2C+5%29%29%5E-1 but then what do you do with that? Perhaps I am going about it the wrong way. Any help would be appreciated, thankyou.
Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
log%28x%2C+5%29+%2B+log%285%2C+x%29+=+2

Let y++=+log%285%2C+x%29,then we have y + 1/y = 2,
so y%5E2-+2y+%2B+1+=+0+
Hence, y = 1 and then x = 5%5Ey+ ???
It is very staightford, I think you can understand.
Kenny