Properties of logarithms
This presentation is the property of its rightful owner.
Sponsored Links
1 / 8

Properties of Logarithms PowerPoint PPT Presentation


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

Properties of Logarithms. Section 3.3. 3.3 PROPERTIES OF LOGARITHMS. Change of base formula: log a x = log b x / log b a = log x / log a = ln x / ln a Evaluate log 9 1043. log 10 1043 / log 10 9 log 1043 / log 9 3.1630 Evaluate using ln: log 9 1043.

Download Presentation

Properties 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


Properties of logarithms

Properties of Logarithms

Section 3.3


3 3 properties of logarithms

3.3 PROPERTIES OF LOGARITHMS

Change of base formula:

loga x = logb x / logb a

= log x / log a

= ln x / ln a

Evaluate log9 1043.

log10 1043 / log10 9

log 1043 / log 9

3.1630

Evaluate using ln: log9 1043.

ln 1043 / ln 9

3.1630 Same!


Properties of logarithms

  • Properties of Logarithms:

    loga (uv) = loga u + loga v

    ln (uv) = ln u + ln v

    loga u/v = loga u – loga v

    ln u/v = ln u – ln v

    loga un = n loga u

    ln un = n ln u


Properties of logarithms

Write each log in terms of ln 2 & ln 3:

  • ln 6

    ln (2 · 3)

    ln 2 + ln 3

  • ln 2/27

    ln 2 – ln 27

    ln 2 – ln 33

    ln 2 – 3 ln 3


Properties of logarithms

  • Verify that – log10 1/100 = log10 100

    -log10 100-1 =

    -(-1) log10 100 =

    log10 100 =

    Expand each expression:

  • log4 5x3y

    log4 5 + log4 x3 + log4 y

    log4 5 + 3 log4 x + log4 y


Properties of logarithms

  • ln √3x – 5

    7

    ln (3x-5)1/2

    7

    ln (3x – 5)1/2 – ln 7

    ½ ln (3x – 5) – ln 7

    Condense each expression:

  • ½ log10 x + 3 log10 (x + 1)

    log x1/2 + log (x + 1)3

    log [ √ x (x + 1)3]


Properties of logarithms

  • 2 ln (x + 2) – ln x

    ln (x + 2)2 – ln x

    ln (x + 2)2

    2

  • 1/3 [log2 x + log2 (x – 4)]

    1/3 {log2 [x(x – 4)]}

    log2 [x(x – 4)]1/3

    log23√ x(x – 4)


Homework

Homework

  • Page 211-213

    10-20 even, 35, 37-55 odd, 72, 74


  • Login