Determine the solutions of the equation lgx1 lg9 1 lgxSol

Determine the solutions of the equation lg(x+1) - lg9 = 1 - lg(x)

To solve lg(x+1)-lg9 = 1-lgx.

We move the unknowns and isolate them:

lg(x+1)+lgx =lo9+1.

lg(x+1)x = log9+log10, as lga+lgb = lgab and as10^1 =1, lg10 = 1,

by definition.

lg(x+1)x = lg9*10

x(x+1) = 9*(10).

x = 9 , obviously satisfies the equation.

x = 9.