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What is the solution of the equation x log10(10/3) + log103 = log10(2 + 3x) + x?

What is the solution of the equation x log10(10/3) + log103 = log10(2 + 3x) + x? Correct Answer 0

x log10(10/3) + log103 = log10(2 + 3x) + x

⇒ x log1010 – x log103 + log103 = log10(2 + 3x) + x

⇒ x – x log103 + log103 = log10(2 + 3x) + x

⇒ log103-x + log103 = log10(2 + 3x)

⇒ log10(3-x) × 3 = log10(2 + 3x)

⇒ (3-x) × 3 = (2 + 3x)

⇒ 3/3x = (2 + 3x)

Suppose 3x = p;

⇒ 3/p = (2 + p)

⇒ p2 + 2p – 3 = 0

⇒ (p + 3) (p – 1) = 0

⇒ p = -3, 1

∴ 3x = 1

⇒ 3x = 30

∴ x = 0

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