What is the solution of the equation
x log10 (10/3) + log10 3 = log10 (2 + 3x) + x?

  1. 10
  2. 3
  3. 1
  4. 0

Answer

x log10 (10/3) + log10 3 = log10 (2 + 3x) + x

x log10 10 - x log10 3 + log10 3 = log10 (2 + 3x) + x

x - x log10 3 + log10 3 = log10 (2 + 3x) + x

log10 3 - log10 3x = log10 (2 + 3x)

log10 (3/3x) = log10 (2 + 3x)

3/3x = 2 + 3x

Let 3x = t

3/t = 2 + t

t2 +2t - 3 = 0

t = -3, 1

3x = 1

x = 0

The correct option is D.

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