Question

If logbase2[logbase7( x^2-x+37)] = 1, then what could be the value of x​

Answer 1

Step-by-step explanation:

• We know that

⤇logₓa = n

⤇ a = xⁿ

• SOLUTION

log₂ [log₇ (x²-x+37) ] = 1

log₇(x² - x + 37) = 2¹ = 2

x² - x + 37 = 7²

x² - x + 37 = 49

x² - x + 37 – 49 = 0

x² - x - 12 = 0

x² - 4x + 3x - 12 = 0

x(x - 4) + 3(x - 4) = 0

(x - 4) (x + 3) = 0

x = 4 or -3