3 Txoj hauv kev los daws Logarithms

2024 Tus sau: Jason Gerald | [email protected]. Kawg hloov kho: 2024-01-15 08:16

Logarithms yuav zoo li nyuaj rau daws, tab sis kev daws teeb meem logarithm yog qhov yooj yim dua li qhov koj xav, vim hais tias logarithms tsuas yog lwm txoj hauv kev sau cov zauv sib npaug. Thaum koj tau rov sau cov logarithm hauv daim ntawv uas paub zoo dua, koj yuav tsum muaj peev xwm daws tau nws zoo li koj xav tau lwm qhov kev sib npaug zoo ib yam.

Kauj ruam

Ua ntej Koj Pib: Kawm Qhia Tawm Logarithmic Equations Exponentially

Kauj Ruam 1. Nkag siab lub ntsiab lus ntawm logarithm

Ua ntej daws qhov sib npaug logarithmic, koj yuav tsum nkag siab tias logarithms yog qhov tseem ceeb lwm txoj hauv kev ntawm kev sau cov zauv nthuav tawm. Lub ntsiab lus tseeb yog raws li hauv qab no:

• y = loga_b (x)

  Yog thiab tsuas yog tias: b^y = xwm

• Nco ntsoov tias b yog lub hauv paus ntawm logarithm. Tus nqi no yuav tsum ua tau raws li cov hauv qab no:

  • b> 0 hli
  • b tsis sib npaug rau 1
• Hauv qhov sib npaug, y yog tus piav qhia, thiab x yog qhov tshwm sim ntawm kev suav qhov nthuav tawm nrhiav hauv logarithm.

Kauj Ruam 2. Xav txog qhov sib npaug logarithmic

Thaum saib qhov sib npaug ntawm qhov teeb meem, saib rau lub hauv paus (b), tus piav qhia (y), thiab nthuav tawm (x).

• Piv txwv:

  5 = logJ₄(1024)

  • b = 4 hli
  • y = 5 hli
  • x = 1024 po

Kauj Ruam 3. Tshem qhov nthuav tawm mus rau ib sab ntawm qhov sib npaug

Tsiv tus nqi ntawm koj qhov kev nthuav tawm, x, mus rau ib sab ntawm qhov sib npaug kos npe.

• Piv txwv li:

  1024 = ?

Kauj Ruam 4. Nkag mus rau tus nqi ntawm tus exponent rau nws lub hauv paus

Koj lub hauv paus tus nqi, b, yuav tsum muab sib npaug los ntawm tus lej zoo ib yam uas sawv cev los ntawm cov lus y.

• Piv txwv:

  4 * 4 * 4 * 4 * 4 = ?

  Qhov sib npaug no tseem tuaj yeem sau ua: 4⁵

Kauj Ruam 5. Sau koj cov lus teb zaum kawg

Tam sim no koj yuav tsum tuaj yeem rov sau qhov sib npaug logarithmic ua qhov sib npaug nthuav tawm. Ob zaug-xyuas koj cov lus teb kom ntseeg tau tias ob sab ntawm qhov sib npaug muaj tus nqi zoo ib yam.

• Piv txwv:

  4⁵ = 1024

Txoj Kev 1 ntawm 3: Nrhiav Tus Nqi ntawm X

Kauj Ruam 1. Sib cais logarithmic equation

Ua qhov kev suav rov qab los txav ib feem ntawm qhov sib npaug uas tsis yog qhov sib npaug logarithmic mus rau lwm sab.

• Piv txwv:

  cav₃(x + 5) + 6 = 10

  • cav₃(x + 5) + 6 - 6 = 10 - 6
  • cav₃(x + 5) = 4x

Kauj Ruam 2. Rov sau qhov sib npaug no hauv daim ntawv nthuav tawm

Siv qhov koj twb paub txog kev sib raug zoo ntawm cov lej logarithmic thiab cov zauv nthuav tawm, thiab rov sau lawv hauv daim ntawv nthuav tawm uas yooj yim dua thiab yooj yim dua los daws.

• Piv txwv:

  cav₃(x + 5) = 4x

  • Sib piv cov zauv no nrog lub ntsiab lus ntawm [ y = loga_b (x)], tom qab ntawd koj tuaj yeem xaus tias: y = 4; b = 3; x = 4x + 5
  • Sau qhov sib npaug li: b^y = xwm
  • 3⁴ = x + + 4x + 5

Kauj Ruam 3. Nrhiav tus nqi x

Thaum qhov teeb meem no tau yooj yim rau qhov yooj yim nthuav dav sib npaug, koj yuav tsum tuaj yeem daws nws ib yam li lwm qhov kev ua zauv nthuav tawm.

• Piv txwv:

  3⁴ = x + + 4x + 5

  • 3 * 3 * 3 * 3 = x + 5
  • 81 = x + + 4x
  • 81 - 5 = x + 5 - 4x
  • 76 = x os

Kauj Ruam 4. Sau koj cov lus teb zaum kawg

Cov lus teb zaum kawg uas koj tau txais thaum koj pom tus nqi x yog lo lus teb rau koj thawj qhov teeb meem logarithm.

• Piv txwv:

  x: 76 ua

Txoj Kev 2 ntawm 3: Nrhiav Tus Nqi ntawm X Siv Txoj Cai Logarithmic Ntxiv Ntxiv

Kauj Ruam 1. Nkag siab cov cai rau kev ntxiv logarithms

Thawj qhov khoom ntawm logarithms hu ua "logarithmic ntxiv txoj cai" hais tias logarithm ntawm cov khoom lag luam sib npaug nrog cov lej ntawm logarithms ntawm ob qhov txiaj ntsig. Sau txoj cai no hauv kab zauv:

• cav_b(m * n) = log_b(m) + log_b(n)

• Nco ntsoov tias cov hauv qab no yuav tsum siv:

  • m> 0 hli
  • n> 0

Kauj Ruam 2. Muab cov logarithm faib ua ib sab ntawm qhov sib npaug

Siv cov lus teb rov qab los txhawm rau txav ib feem ntawm qhov sib npaug kom tag nrho cov lej sib npaug logarithmic nyob ntawm ib sab, thaum lwm qhov khoom siv nyob ntawm lwm sab.

• Piv txwv:

  cav₄(x + 6) = 2 - log₄(x)

  • cav₄(x + 6) + log₄(x) = 2 - log₄(x) + log₄(x)
  • cav₄(x + 6) + log₄(x) = 2

Kauj Ruam 3. Siv txoj cai ntxiv logarithmic

Yog tias muaj ob lub logarithms uas ntxiv rau hauv qhov sib npaug, koj tuaj yeem siv txoj cai logarithm los tso ua ke.

• Piv txwv:

  cav₄(x + 6) + log₄(x) = 2

  • cav₄[(x + 6) * x] = 2
  • cav₄(xwm² (6x + 4x) = 2

Kauj Ruam 4. Rov sau qhov sib npaug no hauv daim ntawv nthuav tawm

Nco ntsoov tias logarithms tsuas yog lwm txoj hauv kev sau cov lej sib npaug. Siv cov ntsiab lus logarithmic rov sau qhov sib npaug rau hauv daim ntawv uas tuaj yeem daws tau.

• Piv txwv:

  cav₄(xwm² (6x + 4x) = 2

  • Sib piv cov zauv no nrog lub ntsiab lus ntawm [ y = loga_b (x)], koj tuaj yeem xaus tias: y = 2; b = 4; x = xwm² + 6x ib
  • Sau qhov kev ua zauv no kom: b^y = xwm
  • 4² = xwm² + 6x ib

Kauj Ruam 5. Nrhiav tus nqi x

Thaum qhov kev ua zauv no tau dhau los ua qhov sib npaug nthuav tawm ib txwm muaj, siv qhov koj paub txog qhov sib npaug nthuav tawm kom pom tus nqi x raws li koj ib txwm xav tau.

• Piv txwv:

  4² = xwm² + 6x ib

  • 4 * 4x = x² + 6x ib
  • 16 = x² + 6x ib
  • 16 - 16 = x² + 4x - 16
  • 0 = x² + 4x - 16
  • 0 = (x - 2) * (x + 8) - 4x
  • x = 2; x = -8

Kauj Ruam 6. Sau koj cov lus teb

Txij ntawm no mus, koj yuav tsum muaj cov lus teb rau qhov sib npaug. Sau koj cov lus teb hauv qhov chaw muab.

• Piv txwv:

  x = 2 os

• Nco ntsoov tias koj tsis tuaj yeem muab cov lus teb tsis zoo rau logarithm, yog li koj tuaj yeem tshem cov lus teb x -8 ib.

Txoj Kev 3 ntawm 3: Nrhiav Tus Nqi ntawm X Siv Txoj Cai Logarithmic Division

Kauj Ruam 1. Nkag siab txog txoj cai faib logarithmic

Raws li qhov khoom thib ob ntawm logarithms, hu ua "logarithmic division rule," logarithm ntawm kev faib tuaj yeem rov sau dua los ntawm kev rho tawm logarithm ntawm tus lej ntawm tus lej. Sau qhov kev ua zauv raws li hauv qab no:

• cav_b(m/n) = log_b(m) - log_b(n)

• Nco ntsoov tias cov hauv qab no yuav tsum siv:

  • m> 0 hli
  • n> 0

Kauj Ruam 2. Muab cov logarithmic equation faib ua ib sab

Ua ntej koj daws qhov kev ua zauv logarithmic, koj yuav tsum hloov tag nrho logarithmic equations mus rau ib sab ntawm qhov sib npaug kos npe. Ib nrab ntawm qhov sib npaug yuav tsum tau txav mus rau lwm sab. Siv cov lej rov qab los daws nws.

• Piv txwv:

  cav₃(x + 6) = 2 + log₃(x - 2)

  • cav₃(x + 6) - log₃(x - 2) = 2 + log₃(x - 2) - log₃(x - 2)
  • cav₃(x + 6) - cov₃(x - 2) = 2

Kauj Ruam 3. Siv txoj cai faib logarithmic

Yog tias muaj ob lub logarithms hauv qhov kev ua zauv, thiab ib qho ntawm lawv yuav tsum raug rho tawm ntawm lwm qhov, koj tuaj yeem thiab yuav tsum siv txoj cai faib los coj ob lub logarithms no ua ke.

• Piv txwv:

  cav₃(x + 6) - log₃(x - 2) = 2

  cav₃[(x + 6) / (x - 2)] = 2

Kauj Ruam 4. Sau qhov sib npaug no hauv daim ntawv nthuav tawm

Tom qab tsuas yog ib qho kev sib npaug logarithmic tseem nyob, siv cov ntsiab lus logarithmic los sau nws hauv daim ntawv nthuav tawm, tshem tawm cov cav.

• Piv txwv:

  cav₃[(x + 6) / (x - 2)] = 2

  • Sib piv cov zauv no nrog lub ntsiab lus ntawm [ y = loga_b (x)], koj tuaj yeem xaus tias: y = 2; b = 3; x = (x + 6) / (x - 2)
  • Sau qhov sib npaug li: b^y = xwm
  • 3² = (x + 6) / (x - 2)

Kauj Ruam 5. Nrhiav tus nqi x

Thaum qhov sib npaug yog nthuav dav, koj yuav tsum muaj peev xwm nrhiav tus nqi x raws li koj ib txwm xav tau.

• Piv txwv:

  3² = (x + 6) / (x - 2)

  • 3 * 3 = (x + 6) / (x - 2)
  • 9 = (x + 6) / (x --2)
  • 9 * (x - 2) = [(x + 6) / (x - 2)] * (x - 2)
  • 9 - 18 = x + 6 - 4x
  • 9 - x - 18 + 18 = x - x + 6 + 18
  • 8 x = 24 po
  • 8/8 = 24/8
  • x = 3 os

Kauj Ruam 6. Sau koj cov lus teb zaum kawg

Tshawb nrhiav thiab tshawb xyuas ob zaug koj cov kauj ruam kev suav. Thaum koj paub tseeb tias cov lus teb raug lawm, sau nws.

• Piv txwv:

  x = 3 os