Elf 01 6 laws of logarithms
This presentation is the property of its rightful owner.
Sponsored Links
1 / 12

ELF.01.6 - Laws of Logarithms PowerPoint PPT Presentation


  • 51 Views
  • Uploaded on
  • Presentation posted in: General

ELF.01.6 - Laws of Logarithms. MCB4U - Santowski. (A) Review. if f(x) = a x , find f -1 (x) so y = a x then x = a y and now isolate y in order to isolate the y term, the logarithmic notation or symbol or function was invented or created so we write x = a y as y = log a (x).

Download Presentation

ELF.01.6 - Laws of Logarithms

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Elf 01 6 laws of logarithms

ELF.01.6 - Laws of Logarithms

MCB4U - Santowski


A review

(A) Review

  • if f(x) = ax, find f -1(x) so y = ax then x = ay and now isolate y

  • in order to isolate the y term, the logarithmic notation or symbol or function was invented or created so we write x = ay as y = loga(x)


B properties of logarithms logarithms of powers

Consider this approach here in column 1

evaluate log5(625) = x

5x = 625

5x = 54

x = 4

Now try log5(625) = x tis way:

log5(54) = x

log5(5)4 = x

Now I know from column 1 that the answer is 4 … so …

log5(5)4 = 4

4 x log5(5) = 4

4 x 1 = 4

(B) Properties of Logarithms- Logarithms of Powers


B properties of logarithms logarithms of powers1

(B) Properties of Logarithms- Logarithms of Powers

  • So if log5(625) = log5(5)4 = 4 x log5(5)

  • It would suggest a rule of logarithms 

  • logb(bx) = x

  • Which we can generalize 

  • logb(ax) = xlogb(a)


C properties of logarithms logs as exponents

(C) Properties of Logarithms – Logs as Exponents

  • Consider the example

  • Recall that the expression log3(5) simply means “the exponent on 3 that gives 5”  let’s call that x

  • So we are then asking you to place that same exponent (the x) on the same base of 3

  • Therefore taking the exponent that gave us 5 on the base of 3 (x ) onto a 3 again, must give us the same 5!!!!

  • We can demonstrate this algebraically as well


C properties of logarithms logs as exponents1

(C) Properties of Logarithms – Logs as Exponents

  • Let’s take our exponential equation and write it in logarithmic form

  • So becomes log3(x) = log3(5)

  • Since both sides of our equation have a log3 then x = 5 as we had tried to reason out in the previous slide

  • So we can generalize that


D properties of logarithms product law

(D) Properties of Logarithms – Product Law

  • Express logam + logan as a single logarithm

  • We will let logam = x and logan = y

  • So logam + logan becomes x + y

  • But if logam = x, then ax = m and likewise ay = n

  • Now take the product (m)(n) = (ax)(ay) = ax+y

  • Rewrite mn=ax+y in log form  loga(mn)=x + y

  • But x + y = logam + logan

  • So thus loga(mn) = logam + logan


E properties of logarithms quotient law

(E) Properties of Logarithms – Quotient Law

  • We could develop a similar “proof” to the quotient law as we did with the product law  except we ask you to express logam - logan as a single logarithm

  • As it turns out (or as is predictable), the simplification becomes as follows:

  • loga(m/n) = loga(m) – loga(n)


F summary of laws

(F) Summary of Laws


G examples

(G) Examples

  • (i) log354 + log3(3/2)

  • (ii) log2144 - log29

  • (iii) log30 + log(10/3)

  • (iv) which has a greater value

    • (a) log372 - log38 or (b) log500 + log2

  • (v) express as a single value

    • (a) 3log2x + 2log2y - 4log2a

    • (b) log3(x+y) + log3(x-y) - (log3x + log3y)

  • (vi) log2(4/3) - log2(24)

  • (vii) (log25 + log225.6) - (log216 + log39)


G internet links

(G) Internet Links

  • Logarithm Rules Lesson from Purple Math

  • College Algebra Tutorial on Logarithmic Properties from West Texas AM


H homework

(H) Homework

  • Nelson textbook, p125, Q1-14


  • Login