Graph the function fx xx2 4 Solve the equation 45 3x 125

Graph the function. f(x) = x/x^2 - 4 Solve the equation. 4(5 - 3x) = 1/256 log_4 (x + 5) + log_4 (x- 1) = 2

Solution

11) 4^{(5 - 3x)} = 1/256 = (1/4)⁴ = (4)^-4

=> 5 - 3x = -4

=> x = 3

12) log₄(x+5) + log₄(x-1) = 2

log₄((x+5)(x-1)) = 2

=> x² + 4x - 5 = (4)²

=> x² + 4x - 21 = 0

=> x = (-4 - sqrt(16 + 84))/2 or   x = (-4 + sqrt(16 + 84))/2

=> x = -7 or x = 3

but x cant be -7 as (x-1) should be greater than 0.

=> x = 3