Find the solution in the simplest form lgx/(1 - lg2) = 2.
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We'll impose the constraints of existence of logarithm.
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.
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