解決13500{left(1+0.075/12right)}^300=x |Microsoft數學求解器

$$13500 { \left(1+ \frac{ 0.075 }{ 12 } \right) }^{ 300 } =x$$

解 x

$$x=87518.8860491627590326575859329702481742577993768798507167667030373301150753629923627622066264437557277728264042399564703709356400030126534364229551611733536088163243290135013593961493135001556996510692355503880344669301384269225644432405592220746538795581161713201413808695994191507831948689191812739440156371985081663700967772186682032691528696981742603391608508408986751409827821678646504243595596088602721384405489317149616339709352792911692809150998914394940630619510416768378292363574561863355092868478128875497338071103081533448708968116552195215527852995351422229201007529193961418496322237455509265198830763657016835884321307323417923709645470930193236726739516211587402315786414015338049866063083222176058346663768388254533665933038360252717519574169970366639838503354658238235386127428684855955831628822819061260946947600894322324710242858089212057018274450844551643142933894469910771071593871499303199137594344433618319672139082103107014236875950944868502466461578483777037530467862307688669351150075225985473278562182196164127125089800727288598801473286183719225958723884191896739273583829161356183930381708247965459292586906589449873463588805126928252367871291332283388004105978666621192613464949190417425547121905038957147723109619402697070403725488319851434346685656025512098443180297577389688046576912311411712240065784340677705915146683615266474683846231777926722013235517283432482151352599574789798809199784249635713690681585226880770278065266830347379567456300719641149044036865234375$$

解線性方程式的步驟

同時對分子與分母乘上 1000 以展開 \frac{0.075}{12}。

$$13500\left(1+\frac{75}{12000}\right)^{300}=x$$

透過找出與消去 75，對分式 \frac{75}{12000} 約分至最低項。

$$13500\left(1+\frac{1}{160}\right)^{300}=x$$

將 1 與 \frac{1}{160} 相加可以得到 \frac{161}{160}。

$$13500\times \left(\frac{161}{160}\right)^{300}=x$$

計算 \frac{161}{160} 的 300 乘冪，然後得到 \frac{111625343813575884206676000744586761890808035155985506069834123483764002987322477421058888939804099998537465127407324193708673481044294128292064216472174576776340661195783961382995346848235325114800899509929633209349834627557832713917693001290796673036013785320050727903147995687117135486713336104985814272526363983478093730021904178361534602389849704817926163314935392854060016711723703890647659359830754551740621091674884189072073202651605133041857514442541408440401280586931282990742561919116008831009220440048797128360935933195988091607189858662139228518639428586818716235212432895111160342131155448428622434655232888512797207229597512196364814744696341808001}{17218479456385750618067377696052635483579924745448689921733236816400740691241745619397484537236046173286370919031961587788584927290816661024991609882728717344659503471655990880884679896520055123906467064419056526231345685268240569209892573766037966584735183775739433978714578587782701380797240772477647874555986712746271362892227516205318914435913511141036261376000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}。

$$13500\times \frac{111625343813575884206676000744586761890808035155985506069834123483764002987322477421058888939804099998537465127407324193708673481044294128292064216472174576776340661195783961382995346848235325114800899509929633209349834627557832713917693001290796673036013785320050727903147995687117135486713336104985814272526363983478093730021904178361534602389849704817926163314935392854060016711723703890647659359830754551740621091674884189072073202651605133041857514442541408440401280586931282990742561919116008831009220440048797128360935933195988091607189858662139228518639428586818716235212432895111160342131155448428622434655232888512797207229597512196364814744696341808001}{17218479456385750618067377696052635483579924745448689921733236816400740691241745619397484537236046173286370919031961587788584927290816661024991609882728717344659503471655990880884679896520055123906467064419056526231345685268240569209892573766037966584735183775739433978714578587782701380797240772477647874555986712746271362892227516205318914435913511141036261376000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}=x$$

將 13500 乘上 \frac{111625343813575884206676000744586761890808035155985506069834123483764002987322477421058888939804099998537465127407324193708673481044294128292064216472174576776340661195783961382995346848235325114800899509929633209349834627557832713917693001290796673036013785320050727903147995687117135486713336104985814272526363983478093730021904178361534602389849704817926163314935392854060016711723703890647659359830754551740621091674884189072073202651605133041857514442541408440401280586931282990742561919116008831009220440048797128360935933195988091607189858662139228518639428586818716235212432895111160342131155448428622434655232888512797207229597512196364814744696341808001}{17218479456385750618067377696052635483579924745448689921733236816400740691241745619397484537236046173286370919031961587788584927290816661024991609882728717344659503471655990880884679896520055123906467064419056526231345685268240569209892573766037966584735183775739433978714578587782701380797240772477647874555986712746271362892227516205318914435913511141036261376000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} 得到 \frac{3013884282966548873580252020103842571051816949211608663885521334061628080657706890368590001374710699960511558439997753230134183988195941463885733844748713572961197852286166957340874364902353778099624286768100096652445534944061483275777711034851510171972372203641369653384995883552162658141260074834616985358211827553908530710591412815761434264525942030084006409503255607059620451216540005047486802715430372896996769475221873104945976471593338592130152889948618027890834575847144640750049171816132238437248951881317522465745270196291678473394126183877759170003264571844105338350735688168001329237541197107572805735691287989845524595199132829301849998106801228816027}{34436958912771501236134755392105270967159849490897379843466473632801481382483491238794969074472092346572741838063923175577169854581633322049983219765457434689319006943311981761769359793040110247812934128838113052462691370536481138419785147532075933169470367551478867957429157175565402761594481544955295749111973425492542725784455032410637828871827022282072522752000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}。

$$\frac{3013884282966548873580252020103842571051816949211608663885521334061628080657706890368590001374710699960511558439997753230134183988195941463885733844748713572961197852286166957340874364902353778099624286768100096652445534944061483275777711034851510171972372203641369653384995883552162658141260074834616985358211827553908530710591412815761434264525942030084006409503255607059620451216540005047486802715430372896996769475221873104945976471593338592130152889948618027890834575847144640750049171816132238437248951881317522465745270196291678473394126183877759170003264571844105338350735688168001329237541197107572805735691287989845524595199132829301849998106801228816027}{34436958912771501236134755392105270967159849490897379843466473632801481382483491238794969074472092346572741838063923175577169854581633322049983219765457434689319006943311981761769359793040110247812934128838113052462691370536481138419785147532075933169470367551478867957429157175565402761594481544955295749111973425492542725784455032410637828871827022282072522752000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}=x$$

換邊，將所有變數項都置於左邊。

$$x=\frac{3013884282966548873580252020103842571051816949211608663885521334061628080657706890368590001374710699960511558439997753230134183988195941463885733844748713572961197852286166957340874364902353778099624286768100096652445534944061483275777711034851510171972372203641369653384995883552162658141260074834616985358211827553908530710591412815761434264525942030084006409503255607059620451216540005047486802715430372896996769475221873104945976471593338592130152889948618027890834575847144640750049171816132238437248951881317522465745270196291678473394126183877759170003264571844105338350735688168001329237541197107572805735691287989845524595199132829301849998106801228816027}{34436958912771501236134755392105270967159849490897379843466473632801481382483491238794969074472092346572741838063923175577169854581633322049983219765457434689319006943311981761769359793040110247812934128838113052462691370536481138419785147532075933169470367551478867957429157175565402761594481544955295749111973425492542725784455032410637828871827022282072522752000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$