Wikipedia:Reference desk/Archives/Mathematics/2015 May 8

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May 8

order of operations

Does $-\log _{10}(7)+3\times \log _{10}(8)=3\times \log _{10}(8)-\log _{10}(7)$?96.52.0.249 (talk) 03:29, 8 May 2015 (UTC)

In both the left and right equation, the quantities represented by the logarithms are real numbers, in essence, you are then asking whether $-a+b=b-a$ for real numbers $a,b$, which it is, and this follows from the associativity of addition (since $b-a=b+(-a)$). 76.14.232.104 (talk) 05:24, 8 May 2015 (UTC)

Yes, in this case there is no other plausible reading. However, the minus sign (-) can sometimes be tricky depending upon whether one treats it as a binary subtraction operator or a unary negation operator, and what precedence one assigns to the latter. For example:

• Almost everyone will interpret 3×10³ - 10² as 3×(10³) - (10²) = 2900.
• However, -10² + 3×10³ will be interpreted by some as (-10)² + 3×(10³) = 100+3000= 3100; while others will interpret it as -(10²) + 3×(10³) = -100+3000= 2900.

Abecedare (talk) 05:52, 8 May 2015 (UTC)

However, only the second interpretation is standard in math. See the article linked in the section title. --174.88.135.200 (talk) 04:50, 9 May 2015 (UTC)

So the second bullet represents a or the unary (explain) negation (explain) operator (explain)?96.52.0.249 (talk) 09:11, 9 May 2015 (UTC)

You can see wikipedia's articles on unary operation and negation for an explanation of those terms, or you can just ignore the jargon since what I am referring to is the simple operation of reversing the sign of a number, ie turning b into -b (eg, a 3 into -3) by prefixing a minus sign.

And 174* is correct that only the second interpretation (-10² + 3×10³ = -(10²) + 3×(10³) = -100+3000) is standard in math. It's just an unfortunate fact that not everyone follows this standard, so it is useful to be aware of the possibility and use parenthesis to avoid potential misinterpretation. Abecedare (talk) 04:08, 10 May 2015 (UTC)

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One plus one?

What is 1+1? — Preceding unsigned comment added by 73.189.208.68 (talk) 19:03, 8 May 2015 (UTC)

See 1+1 or Addition. PrimeHunter (talk) 00:08, 9 May 2015 (UTC)

Or Principia Mathematica. --174.88.135.200 (talk) 04:52, 9 May 2015 (UTC)