Question

find the nature of the root of log2^(3–x)+log2^(1–x)=3

Answer 1

Answer:

x = 5, - 1

Step-by-step explanation:

Given to find the nature of the root of log2^(3–x)+log2^(1–x)=3

log 2^(3 - x) + log 2^(1 - x) = 3

log₂(3 - x) (1 - x) = 3

log₂( 3 - x - 3x + x^2) = 3

2^3 = x^2 - 4x + 3

8 = x^2 - 4x + 3

x^2 - 4x -5 = 0

x^2 - 5x + x - 5 = 0

x(x - 5) + 1(x - 5) = 0

(x - 5)(x + 1) = 0

x = 5, -1

Nature of roots are one is positive and another is negative.