LOGARITHMS

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# LOGARITHMS - PowerPoint PPT Presentation

LOGARITHMS. Another way to play with EXPONENTS. DEFINITION. What is it…. A LOGARITHM IS AN EXPONENT. If x = b y then log b (x) = y. PROPERTIES. What makes a logarithm tick!. MULTIPLICATON ADDITION.

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## PowerPoint Slideshow about 'LOGARITHMS' - natala

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Presentation Transcript

### LOGARITHMS

Another way to play with EXPONENTS

DEFINITION

What is it…

A LOGARITHM IS AN EXPONENT
• If x = by then logb(x) = y
PROPERTIES

What makes a logarithm tick!

• A major property of logarithms is that they map multiplication to addition, as a result of the identity

bxx by = b(x + y)

• which by taking logarithms becomes

logb(bx x by) = logb(b(x + y)) = x + y = logb(bx) + logb(by)

TAKING THE LOG OF AN EXPONENT
• If you take the log of a number with an exponent, the exponent becomes a coefficient!
• logb(cp) = p logb(c)
NATURAL LOGARITHMS and COMMON LOGARITHMS
• A logarithm can have any base
• We will concentrate on 2
• Common Logs have a base of 10
• log104 is written as log 4
• Natural Logs have a base of e
• e = 2.7182818…
• Also called Euler’s Number after Leonhard Euler
• loge4 is written as ln 4
EVEN MORE PROPERTIES

More exponential behavior…

PRODUCTS
• logbmn = logbm + logbn
• For example: log (3· 4) = log 3 + log 4
QUOTIENTS
• Division becomes subtraction
• logb = logbm - logbn
• Example: log = log 4 – log3
TRY THIS…
• log4(64y6)1/3 = ?
FINAL TRICKS

A few more things to know…

HOW TO CALCULATE
• Your calculator has a button for common and natural logs.
• Other logs can use the following property:
• log6 x = (log x)/(log 6)
TRANSFORMATIONS-TRANSLATION
• Compare y = log x to y = log (x + 2)
• Compare y = log x to y = (log x) + 2
TRANSFORMATIONS-DILATION
• Compare y = log x to y = 2 log x