Question

Log_10(x-3) upon log_10( xsquare - 21) = 1 upon 2

Answer 1

Solution :

Given : log₁₀(x - 3) / log₁₀(x² - 21) = 1/2

⇒ 2 log₁₀(x - 3) = log₁₀(x² - 21)

⇒ log₁₀(x - 3)² = log₁₀(x² - 21)

⇒ (x - 3)² = x² - 21

⇒ x² - 6x + 9 = x² - 21

⇒ 6x = 9 + 21 = 30

∴ x = 5 , which is the required solution.

Logarithmic rules :

  • logₐA + logₐB = logₐ(AB)

  • logₐA - logₐB = logₐ(A/B)

  • logₐA = logₐB ⇒ A = B

  • logₐAᵇ = b logₐA

Answer 2

Answer:

Step-by-step explanation: