solve for x, 1/5-logx + 2/1+logx = 1

Answer 1

First add these fractions,

When we find common denominator; we get 1+logx+10-2logx = 5+5logx-logx-logx²

if you solve this equation, you will end up logx2 - 5logx +6=0

lets say logx=y

we get y²-5y +6 = 0 you need to factor this polynomial

y² gives us y*y

6 gives us -6*-1 or -2*-3 (I chose negative factors because I need to add the factors to get -5 which is in the middle)

-6+-1=-7

-2+-3=-5 (we have to choose these factors)

y²-5y +6 =(y-2)(y-3) = 0 in this case

y-2 = 0 and y=2......logx=2

y-3 = 0 and y=3......logx=3