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Question

Find the domain of definition of the following function:
y=logx2(x28x+15).

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Solution

logx2(x28x+15)0x2x28x+151x(,2+4)(4+2,)
and
x2>1x>3x(3,)
and
0<x28x+151 and 0<x2<1
(x3)(x5)>0 and x28x+140
x(,3)(3,) x(42,4+2)
x>2 and x<3
x(2,3)
Taking intersection, we get
x(42,3)(4+2,)

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