# logarithms: solve log5(x)+(log5(125)/log5​(x))=7/2 for x

#### newuser

##### New member
solve for x:
log5(x)+(log5(125)/log5​(x))=7/2

#### Ishuda

##### Elite Member
solve for x:
log5(x)+(log5(125)/log5​(x))=7/2
Suppose you let
y=log5(x)
and 'simplified' the equation to
y2 - (7/2) y + log5(125) = 0

#### newuser

##### New member
Suppose you let
y=log5(x)
and 'simplified' the equation to
y2 - (7/2) y + log5(125) = 0
Solving for y gives me 9/4 and 5/4
and then for x gives me 25(5)1/2 and 25 resp.

Pls tell me if I'm correct?
The answer in the book is 5 and 5(25)1/2(=25 I calculated,not mentioned in book)

Thanks for your help

#### newuser

##### New member
Solving for y gives me 9/4 and 5/4
and then for x gives me 25(5)1/2 and 25 resp.

Pls tell me if I'm correct?
The answer in the book is 5 and 5(25)1/2(=25 I calculated,not mentioned in book)

Thanks for your help
sorry I got y=2 and 3/2
x=25 and 5(5)1/2​ resp.

#### Ishuda

##### Elite Member
sorry I got y=2 and 3/2
x=25 and 5(5)1/2​ resp.
Which is what I got. If you put those values back in the original equation, i.e. check the answer, I find those are the proper solution.