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Vilka [71]
3 years ago
7

Identify a solution of the equation: log2x+log(x−5)=2

Mathematics
1 answer:
Harrizon [31]3 years ago
6 0

Answer:

  • 3.x= 10

Step-by-step explanation:

  • log 2x + log (x - 5) = 2
  • log (2x(x - 5)) = 2
  • 2x(x - 5) = 10²
  • 2(x² - 5x) = 100
  • x² - 5x - 50 = 0
  • x² + 5x - 10x - 50 = 0
  • x(x + 5) - 10(x + 5) = 0
  • (x - 10)(x + 5) = 0
  • x = 10
  • x = -5, this root is discounted as log should be positive.

Correct choice is 3.

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<img src="https://tex.z-dn.net/?f=x%20%20%5Cdiv%203x%20-%202%20%3D%201%20%5Cdiv%203x%20-%204" id="TexFormula1" title="x \div 3x
Maurinko [17]

Hello from MrBillDoesMath!

Answer:

x = 1/2 (1 +\- i sqrt(23))

Discussion:

x \3x - 2 =   (x/3)*x - 2   =  (x^2)/3 - 2     (*)

1 \3x - 4   =  (1/3)x - 4                               (**)

(*) = (**)   =>

(x^2)/3 -2 = (1/3)x - 4        => multiply both sides by 3

x^2 - 6 = x - 12                 => subtract x from both sides

x^2 -x -6 = -12                   => add 12 to both sides

x^2-x +6  = 0

Using the quadratic formula gives:

x = 1/2 (1 +\- i sqrt(23))

Thank you,

MrB

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