log
(1 - x) - log (x) = 1

In this question, quotient rule is used.

log (m/n) = log (m) - log (n)

__Let 1 - x = m, x = n:__

log
(m) - log (n) = 1

__Using quotient rule:__

log (m/n) = log (m) - log (n) =1

log ((1-x)/x) =1

__Convert logarithm to exponent form:__

log x(y) = z

x^{z}=y

log10((1-x)/x) = 1

(1-x)/x=10

x (1-x)/x=10x (multiply x on both sides)

1-x=10x

1-x+x=10x+x (add x on both sides)

11x=1

11x/11=1/11(divide 11 on both sides)

x=1/11