I find this property of logarithms quite confusing.
$$(-\log x)^2 = (\log x)^2$$
Can also be
$$(-\log x)^2 = \Big(\log \big(\tfrac{1}{x}\big)\Big)^2$$
Which one is correct?
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Both are correct. Why is that confusing? – Jeppe Stig Nielsen Feb 23 '18 at 10:14
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Both are correct. It all stems from the identity $-1\cdot-1=1$. – Parcly Taxel Feb 23 '18 at 10:14
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@Jeppe oh okay then, I got confused since I thought one of them had to be wrong to match the answer given in my TB. Thanks – Anshul Laikar Feb 23 '18 at 10:16
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@ParclyTaxel thank you for helping – Anshul Laikar Feb 23 '18 at 10:17
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What are you solving? – Feb 23 '18 at 10:38
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I was solving integrals with logarithms in them – Anshul Laikar Feb 23 '18 at 10:41
1 Answers
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Both are correct.
The first one is not a property of logarithms, it's a property of squares. (-a)²=a² for all a.
The second one follows from the first because log(1/x) = log(x⁻¹) = -log(x)
Klas
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