# 8.5 Properties of logarithms - PowerPoint PPT Presentation

1 / 11

8.5 Properties of logarithms. p. 493. Properties of Logarithms. Let b, u, and v be positive numbers such that b ≠1. Product property: log b uv = log b u + log b v Quotient property: log b u/v = log b u – log b v Power property: log b u n = n log b u. Use log 5 3 ≈.683 and log 5 7≈1.209.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

8.5 Properties of logarithms

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 - - - - - - - - - - - - - - - - - - - - - - - - - -

## 8.5Properties of logarithms

p. 493

### Properties of Logarithms

• Let b, u, and v be positive numbers such that b≠1.

• Product property:

• logbuv = logbu + logbv

• Quotient property:

• logbu/v = logbu– logbv

• Power property:

• logbun = n logbu

### Use log53≈.683 and log57≈1.209

• Approximate:

• log53/7 =

• log53 – log57 ≈

• .683 – 1.209 =

• -.526

• log521 =

• log5(3·7)=

• log53 + log57≈

• .683 + 1.209 =

• 1.892

• Approximate:

• log549 =

• log572 =

• 2 log57 ≈

• 2(1.209)=

• 2.418

### Expanding Logarithms

• You can use the properties to expand logarithms.

• log2 =

• log27x3 - log2y =

• log27 + log2x3 – log2y =

• log27 + 3·log2x – log2y

• Expand:

• log 5mn=

• log 5 + logm + logn

• Expand:

• log58x3 =

• log58 + 3·log5x

### Condensing Logarithms

• log 6 + 2 log2 – log 3 =

• log 6 + log 22 – log 3 =

• log (6·22) – log 3 =

• log =

• log 8

• Condense:

• log57 + 3·log5t =

• log57t3

• Condense:

• 3log2x – (log24 + log2y)=

• log2

### Change of base formula:

• u, b, and c are positive numbers with b≠1 and c≠1. Then:

• logcu =

• logcu = (base 10)

• logcu = (base e)

### Examples:

• Use the change of base to evaluate:

• log37 =

• (base 10)

• log 7 ≈

• log 3

• 1.771

• (base e)

• ln 7≈

• ln 3

• 1.771