Question

If log₃{log₆(x²+ x/x - 1)} = 0 then x = (a) -1 (b) 1 (c) 3 (d) 4

Answer 1

Answer: -1

Step-by-step explanation:

(I cannot use subscript, so I am using simple number for base instead. Please adjust. Thanks)

If the whole expression is 0, then

log6([x² + x]/[x - 1] = 1 (Because if logx = 0 then x is 1)

Now if this is equal to 1, then (x² + 1)/(x - 1) = 6

Therefore, by cross multiplication:

x² + 1 = 6x - 6

x² - 6x + 7 = 0

x² - 7x + x - 7 = 0

x(x - 7) + 1(x - 7) = 0

(x + 1)(x - 7) = 0

So x = 7 or -1

According to options, x = -1

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