Grade 11Algebra
I x-1l^[(Lnlxl)^2-Lnx^2]=lx-1l^3;find the value of x.Sir could you clear why not to equate Lnlxl^2-Lnx^2 =3?
1 Answer
Vikas TU
Case 1: when 0
U can equate (Lnlxl)^2-Lnx^2 =3
U can equate (Lnlxl)^2-Lnx^2 =3
or let logx = t
t^2 – 2t – 3 = 0
it has roots
t = -1 and t = 3
thus,
logx = -1 and logx = 3
and
x = 1/e
for x = e^3 solution rejected as e^3 is > 1.
Case 2: when x> 1
Again, t will have two roots as:
t = -1 and t = 3
x = 1/e and x = e^3
For x > 1 1/e is rejected and x = e^3 is accepted.
Now intersection for both cases dnot satisfies them simulatneously.
Thus (Lnlxl^2)-Lnx^2 =3
cannot be equated.
Thus it helps!
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