3.3 Properties of Logarithms

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3.3 Properties of Logarithms - PowerPoint PPT Presentation

3.3 Properties of Logarithms. Change of base formula. log a x =. or. Ex. log 4 30 =. 2.4534. 3.8074. log 2 14 =. Properties of Logarithms. 1. log a (uv) = log a u + log a v. 1. ln(uv) = ln u + ln v. 2. log u/v = log a u – log a v. 2. ln u/v = ln u – ln v.

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3.3

Properties of Logarithms

Change of base formula

loga x =

or

Ex. log4 30 =

2.4534

3.8074

log2 14 =

Properties of Logarithms

1. loga (uv) = loga u + loga v

1. ln(uv) = ln u + ln v

2. log u/v = loga u – loga v

2. ln u/v = ln u – ln v

3. loga un = n loga u

3. ln un = n ln u

Use the logarithmic properties to expand the following.

log10 5x3y

= log 5 + log x3 + log y

= log 5 + 3log x + log y

ln (3x – 5)1/2 – ln 7

ln 1 – (ln x + ln y) =

- ln x – ln y

0

Condensing a log function

2 ln (x + 6) + ln x =

ln x(x + 6)2

ln x - ln y + ln z =