Solve the equation lg(x + 1) - lg9 = 1 - lg(x) .

Expert Answers

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log(x+1)-log9 = 1-log(x)

We know that logx-logy= log(x/y)

and log10 =1

Substitute:

log(x+1)/9 = log10-log(x)

log(x+1)/9 = log(10/x)

==> (x+1)/9 = 10/x

==> x(x+1)= 90

==> x^2+x -90=0

Factorize:

(x+10)(x-9)=0

x1=-10  which is impossible because logx ca not be negative.

x2= 9

 

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