Question

Hello! I was wondering how I would solve this problem .
`log_(11)(35 + 3x { }^(2) ) = log_(11)(4x ^(2) - 2x)`

Answer 1

Answer: x = 7 or -5

Step-by-step explanation

Log₁₁(35 + 3x²) = Log₁₁(4x² - 2x)

⇒ 35 + 3x² = 4x² - 2x

4x² - 2x = 3x² + 35

By grouping th terms,

4x² - 3x² - 2x - 35 = 0

x² - 2x - 35 = 0

By factorization, we have

x² - 7x + 5x - 35 = 0

x(x-7) + 5(x-7) = 0

(x-7)(x+5) = 0

Either x-7 = 0 or x+5 = 0

∴ x = 7 or -5