Nā waiwai o logarithms, a kupaianaha - e hiki mai ana i ...

Ka nele no ka Me iʻikeʻia i loko o kanaka koke, i koke me ia ua hiki ke quantify i nā mea a puni ona. Ua hiki ke ea i ka laupaʻi loiloi 'kūpili ke kiʻekiʻe o alakai aku ai i ka "hui-unuhi i" ka pono no ke' ano o ka ho omaulia. Kēia mau mea a me ke kapuai mau i ki initially - a pau'ē aʻe manipulations me ka nui ike like multiplication, puunaue, exponentiation , etc. - he mea "mechanization" o kekahi computational algorithms, a i ka nānā 'ana ma luna o na mea makemakika - "pa-unuhi". Ka mea a ka mea, ua, akā, no ka hanaia'na o algorithms no ka Me mea he nui e piʻi like o ka manaʻo, a me kā lākou kākau, e mau loa haʻalele lākou mark i loko o ka hoomanao ana o na kanaka.

Eono a ehiku kenekulia aku nei i loko o ka mahinaʻai o malina hoʻokele a me ka kilohōkū ua mahuahua ka pono no ka nui dala o ka ho, i mea ole kahaha ko oukou naau, mai ka mea, ua ike i ka Middle Ages ka hooulu ana o ka hoʻokele a me ka kilohōkū. Ma ka malama ana a me ka hopuna'ōlelo "koi breeds lako" mau mathematicians i ka manao - e puku i ka lahui hana-mālama nui ana o ka hoonui mau loa i ka mea hou (dually noʻonoʻo i ka manao e puku i ka papa ma ka subtraction). I ka hana ana i na mana o ka hou Me'ōnaehana i hoʻonohoʻia mai i loko o 1614 ma ka hana o Dzhona Nepera me ka loa kupaianaha inoa "Description o ka papaʻaina kupaianaha o logarithms." O ka holo ana, hele aku la ia, a ma luna o ka hou ia hana o ka hou oihana, akā, ua hoʻonoho mai i ka walaʻauʻana waiwai o logarithms hou Napier. I ka manaʻo o ka helu ana'ōnaehana ka hoʻohana logarithms ua ia ina he moʻo o nā helu 'ano apau loa he geometric Holomua, kā lākou mau logarithms i hana i ka Holomua, akā, makemakika. Ma ke alo o ka mālama '-papahana papa hou iaoia o ka hooponopono Nohie na helu, a me ka mea mua kiʻiaka rula (1620 makahiki) ua paha mua kahiko a me ka nui efficient me ka m'kini helu - ka paʻa mau' enekinia, kila.

No ka pioneering ke alanui manawa me potholes. Initially, ka Olelo Kikeke Ma o ka waihona ipu, ua laweʻia ana, a me ka i ka ho omaulia pololei ua haʻahaʻa, akā, ua i ka 1624 i ka maemae e ai me ka kekimala kumu i paʻiʻia. i loko o ka waiwai o logarithms maiʻano nui hoomaopopo ana: Olelo Kikeke Ma o ka e - C mea he helu a, i ka wa a ke degere o ka Olelo Kikeke Ma waihona ipu (helu A), kūpono ma ka helu o ka b. Classic hoʻopaʻa 'ia e koho nana e like: logA (b) = C - i heluhelu ia penei: b Olelo Kikeke Ma, a hiki i ka waihona ipu A, o ka helu o C. I mea e hana i ka hana ka hoʻohana' ana i ka ole loa ai maʻamau, pālākiō helu, e pono e ike i ka lākou o na rula, i kapa ia "waiwai logarithms. " Ma rula, a pau lula ka mea, he pono ole, subtext - pehea e hoʻokomo, unuhi a me ka ho ololi logarithms. Ano, ua ike i ka hana ia.

Pālākiō waiwai 'Aʻohe a me kekahi

1. logA (1) = 0, ka Olelo Kikeke Ma o ka helu o 1, ua like ia 0 no kekahi kumu - kekahi ma muli o ka helu e hoalaia i Aʻohe loa.

2. logA (A) = 1, o ka ia Olelo Kikeke Ma me ka waihona ipu helu mea 1 - ua kekahi ua kaulana oiaio no kekahi helu o ka mana mua.

Eia hou kekahi a me subtraction o logarithms

3. logA (m) + logA (N) = logA (m * N) - i ka huina o logarithms o ka Olelo Kikeke Ma o kekahi mau helu o ka hana.

4. logA (m) - logA (N) = logA (m / n.) - i ke koena unuhi o na logarithms o ka nui, like me ka mea mua kekahi, ua like me ka Olelo Kikeke Ma o ka lākiō o kēia mau helu.

5. logA (1 / N) = - logA (N), i ka Olelo Kikeke Ma o ka inverse o ka Olelo Kikeke Ma o keia helu, ua like ia "hua". He oluolu ke ike i keia mea i ka hopena o ka muaʻana 4 No ka m = 1.

He oluolu, e hai i na rula i kauoha mai 3-5 ma na aoao a elua o ka ia log kumu.

Nā exponents ma ka pālākiō hua'ōlelo

6. logA (HI) = N * logA (m), i ka Olelo Kikeke Ma o ka helu o ke degere N mea like me ka Olelo Kikeke Ma o keia helu, hoonuiia e ka exponent n.

7. log (AC) (b) = (1 / c) * logA (b), ua heluhelu ia "ka Olelo Kikeke Ma o ka e, ina i ke kumu i ka palapala AC, ua like me ka huina hoonui o ka Olelo Kikeke Ma me ka waihona ipu b. A me A helu o aʻe pela aku».

Haʻilula hoʻololi Olelo Kikeke Ma kumu

8. logA (b) = - logC (b) / logc (A), i ka Olelo Kikeke Ma o ka helu e ana i ka waihona ipu A ma ke hoʻololi i ka waihona ipu C he pōpilikia me ka puu hapa o ka Olelo Kikeke Ma a hiki i ke kumu e, a me ka Olelo Kikeke Ma i ka waihona ipu helu like me ka kekahi waihona ipu A, a me ka hoailona "hua".

Ka luna logarithms a me kā lākou mau waiwai ae no i kupono noi e Nohie i ka i ka ho omaulia ana o ka nui laulā huihui ikehu lā, i laila hoemi i ka manawa o ka laulā ho, a ua hoakaka pono pololei.

Ia mea e kahaha ko oukou naau i ka 'epekema a me ka hana' enekinia, ka waiwai o logarithms i hoʻohana no ka nui maoli e hoohalike ai o physicalʻike manaʻo. No ka laʻana, lohe nuiʻia e hoʻohana i pili cia - decibels ia ana kani pinepine 'a me ka malamalama i loko o ke kālaikūlohea, o ka piha nui i loko o kilohōkū ma ka pH ma ka kemika a me na mea e ae.

Hopenaʻoi loa pālākiō computation hiki wawe ka huli ina lawe, no ka laʻana, a no ka hoonui huahelu elima-helu 3 "hana lima" (i loko o ke kolamu), ka hoʻohana papa o logarithms ma luna o ka pepa o ka pepa, a me ka kiʻiaka alii. Lawa ia i ka olelo ia ma ka la mahope hihia, i ka i ka ho omaulia e lawe ma luna o ka ikaika o 10 kekona He aha ka loa kahaha ko oukou naau, oia ka mea i loko o ke kēia me ka m'kini helu i kēia mau hoʻomaulia lawe manawa,ʻaʻole emi.