Properties Of Indices And Logarithms
Akopọ
Indices and logarithms are two sides of the same coin. One tells you the result of repeated multiplication; the other asks which power produced a given result. Together they unlock a toolkit for simplifying expressions, solving exponential equations and converting between bases that appears throughout the Further Pure Mathematics course.
In this topic you will master the seven index laws, the four core logarithm laws, the change of base formula, and the technique for solving equations where the unknown sits in the exponent. Every rule is derived from the same principle, so once you see the pattern the whole system clicks into place.
Awọn Afojusun
- Use and apply properties of indices and logarithms, including change of base
- Know that log_a(xy) = log_a(x) + log_a(y)
- Know that log_a(x/y) = log_a(x) - log_a(y)
- Know that log_a(x^k) = k log_a(x)
- Know that log_a(a) = 1 and log_a(1) = 0
- Solve equations of the form a^x = b
- Use the change of base formulae
Àwòrán ọpọlọ
A ti ṣe àwòrán kókó yìí kí o lè rí bí àwọn èrò ṣe so pọ̀.
Ṣí àwòrán ọpọlọ nínú áàpù
Káàdì ìrántí
Ìdánrawò kíákíá lórí ohun tí wọ́n ń dán wò nínú kókó yìí.
Ṣe ìdánrawò káàdì wọ̀nyí nínú áàpù
Akọ̀wé Ẹ̀kọ́
Àkọsílẹ̀ Ẹ̀kọ́ Pípé wà lórí Ohun Èlò Green Bridge
Gba ohun èlò Green Bridge CBT sórí fóònù tàbí kọ̀mpútà rẹ fún gbogbo ilé ìkàwé IGCSE: ìwé ìdánwò àtijọ́, ìlànà ìdíwọ̀n, àwòrán èrò, káàdì ìkẹ́kọ̀ọ́ àti ẹ̀kọ́ ohùn.
Ìdánwò Ẹ̀kọ́
Oriire fun ipari ẹkọ lori Properties Of Indices And Logarithms. Ni bayi ti o ti ṣawari naa awọn imọran bọtini ati awọn imọran, o to akoko lati fi imọ rẹ si idanwo. Ẹka yii nfunni ni ọpọlọpọ awọn adaṣe awọn ibeere ti a ṣe lati fun oye rẹ lokun ati ṣe iranlọwọ fun ọ lati ṣe iwọn oye ohun elo naa.
Iwọ yoo pade adalu awọn iru ibeere, pẹlu awọn ibeere olumulo pupọ, awọn ibeere idahun kukuru, ati awọn ibeere iwe kikọ. Gbogbo ibeere kọọkan ni a ṣe pẹlu iṣaro lati ṣe ayẹwo awọn ẹya oriṣiriṣi ti imọ rẹ ati awọn ogbon ironu pataki.
Lo ise abala yii gege bi anfaani lati mu oye re lori koko-ọrọ naa lagbara ati lati ṣe idanimọ eyikeyi agbegbe ti o le nilo afikun ikẹkọ. Maṣe jẹ ki awọn italaya eyikeyi ti o ba pade da ọ lójú; dipo, wo wọn gẹgẹ bi awọn anfaani fun idagbasoke ati ilọsiwaju.
- Simplify a^5 x a^(-2). A) a^10 B) a^7 C) a^3 D) a^(-10) Answer: C
- What is the value of 16^(3/4)? A) 4 B) 8 C) 12 D) 64 Answer: B
- Which expression is equivalent to log_a(x) + log_a(y)? A) log_a(x + y) B) log_a(xy) C) log_a(x^y) D) (log_a x)(log_a y) Answer: B
- What is the value of log_5(1)? A) 5 B) 1 C) 0 D) -1 Answer: C
- If 2^x = 10, which expression gives x? A) log 2 / log 10 B) log 10 / log 2 C) 10 / 2 D) 2 / 10 Answer: B
Ṣiṣẹ́ lórí àwọn ìbéèrè wọ̀nyí nínú ohun èlò náà
Ṣiṣẹ́ lórí àwọn ìbéèrè wọ̀nyí nínú ohun èlò náà
Awọn Iwe Itọsọna Ti a Gba Nimọran
Ẹ̀kọ́ síwájú láti àwọn orísun ṣíṣí
-
Abala ìwé ẹ̀kọ́
Logarithmic Properties
Use the product rule for logarithms.
"College Algebra: Logarithmic Properties" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/college-algebra/pages/6-5-logarithmic-properties. Access for free at https://openstax.org/books/college-algebra/pages/1-introduction
-
Abala ìwé ẹ̀kọ́
Exponential and Logarithmic Equations
Use like bases to solve exponential equations.
"College Algebra: Exponential and Logarithmic Equations" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/college-algebra/pages/6-6-exponential-and-logarithmic-equations. Access for free at https://openstax.org/books/college-algebra/pages/1-introduction
Àwọn àjọ mìíràn ló tẹ̀ wọ́n jáde lábẹ́ ìwé àṣẹ ṣíṣí, a sì dá wọn lọ́lá bí wọ́n ṣe béèrè. Àwọn ìjápọ̀ ń ṣí ojú òpó wọn.
Ṣe Adaṣe Awọn Ibeere Idanwo Adaṣe
Ṣe o fẹ ṣe adaṣe awọn ibeere idanwo adaṣe nipa Properties Of Indices And Logarithms? Ṣe igbasilẹ ohun elo Green Bridge CBT lati wọle si awọn ibeere idanwo adaṣe ati awọn ayẹwo adaṣe kikun fun koko-ọrọ yii.
Ṣe igbasilẹ ohun elo naa lori Google Playstore
Gbogbo ohun ti o nilo lati ṣe dara julọ ninu JAMB, WAEC ati NECO.
