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
xz=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