Logarithms 18/2/2013

= 2 loga x

Properties of Logarithms

Examples

1. loga x2 = loga (x • x)

Coincidence ?

logb xr = r logb x

Power Rule for Logarithms

= loga x + loga x

Logarithms 28/2/2013

logb xr = logb (br m)

Properties of Logarithms

Consider logb x = m

for x, b positive, b ≠ 1

logb xr = r logb x

and (bm)r = xr

= r m = r logb x

, for any real r Now

bm = x = brm

Power Rule for Logarithms

Logarithms 38/2/2013

log 2x

Example 2. log 2x + log (x + x) + log (3x – x)

Properties of Logarithms

3

Question:Is there a relationship between the

= (log 2x + log 2x) + log 2x

= log 4x2 + log 2x

= log 8x 3 = log (2x)

Coincidence ?

3=

33

exponent and the factor ?

OR