Question

log [1 – {1 – (1 – x2)–1}–1]–1/2 can be written as

Answer 1

Forget log and concentrate inside brackets. Start from innermost round bracket.

-1 power means reciprocal of the quantity

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[1 - {1 - (1 - x2 ) -1 }-1 ]-1/2

(1 - x2 ) -1 can be written as 1 / (1 - x2)

[1 - {1 - 1 / (1 - x2) }-1 ]-1/2

[1 - {(1 - x2 - 1) / (1 - x2) }-1 ]-1/2

[1 - {- x2 / (1 - x2) }-1 ]-1/2

[1 - {(1 - x2) / (-x2)} ]-1/2

[1 + {(1 - x2) / x2} ]-1/2

[(x2 + 1 - x2) / x2 ]-1/2

[1/x2 ]-1/2

[x2]1/2

√x2

x

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So according to my solution, the answer should be logx