# lgx/(1 - lg2) = 2.Find the solution in the simplest form lgx/(1 - lg2) = 2.

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### 1 Answer

We'll impose the constraints of existence of logarithm.

x>0

The solution has to be in the interval of admissible values (0,+infinite)

lgx/(1-lg2) = 2

lgx = 2 - 2*lg2

Well use the power rule of logarithms for 2*lg2:

a*lg b = lg b^a

2*lg2 = lg 2^2 = lg 4

lgx = 2 - lg 4

But 2 = 2*1 = 2lg 10 = lg 10^2 = lg 100

We'll re-write the equation:

lgx = lg 100 - lg 4

We'll use the quotient rule of logarithms:

lg 100 - lg 4 = lg 100/4

lg 100 - lg 4 = lg 25

lgx = lg 25

Since the bases are matching, we'll apply one to one rule:

x = 25

Since the solution belongs to the interval of admissible value, we'll accept it.