Properties Of Indices And Logarithms
Gbogbo ọrọ náà
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.
Ebumnobi
- 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
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Ekele diri gi maka imecha ihe karịrị na Properties Of Indices And Logarithms. Ugbu a na ị na-enyochakwa isi echiche na echiche ndị dị mkpa, ọ bụ oge iji nwalee ihe ị ma. Ngwa a na-enye ụdị ajụjụ ọmụmụ dị iche iche emebere iji kwado nghọta gị wee nyere gị aka ịmata otú ị ghọtara ihe ndị a kụziri.
Ị ga-ahụ ngwakọta nke ụdị ajụjụ dị iche iche, gụnyere ajụjụ chọrọ ịhọrọ otu n’ime ọtụtụ azịza, ajụjụ chọrọ mkpirisi azịza, na ajụjụ ede ede. A na-arụpụta ajụjụ ọ bụla nke ọma iji nwalee akụkụ dị iche iche nke ihe ọmụma gị na nkà nke ịtụgharị uche.
Jiri akụkụ a nke nyocha ka ohere iji kụziere ihe ị matara banyere isiokwu ahụ ma chọpụta ebe ọ bụla ị nwere ike ịchọ ọmụmụ ihe ọzọ. Ekwela ka nsogbu ọ bụla ị na-eche ihu mee ka ị daa mba; kama, lee ha anya dị ka ohere maka ịzụlite onwe gị na imeziwanye.
- 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
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Akụkụ akwụkwọ
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
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Akụkụ akwụkwọ
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
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