Question

The number of solutions of log10(7x - 12 - x²) = log10 (23 - 5x) is

(A) 0

(C) 2

(B) 1

(D) Infinite​

Answer 1

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Answer 2

(c) is the correct answer.

Given: log₁₀(7x - 12 - x²) = log₁₀(23 - 5x)

To find: Number of solutions

Solution:

We are given that

log₁₀(7x - 12 - x²) = log₁₀(23 - 5x)

⇒ 7x - 12 - x² = 23 - 5x [∵ Same base]

⇒ x² - 5x - 7x + 23 + 12 = 0

⇒ x² - 5x - 7x + 35 = 0

⇒ x(x - 5) - 7(x - 5) = 0

⇒ (x - 7)(x - 5) = 0

⇒ x = 7 or x = 5

⇒ Number of solutions = 2

∴ (c) is the correct answer.

SPJ2