Pre-Calc
Wednesday, November 12, 2008
Section 5.5: Logarithmic Functions
Common logarithm of a positive real number x:
The exponent when the number is written as a
power of 10.
log10 x = a if and only if 10a = x
Examples:
100 =
102 =
105 =
log 1,000 =
log 1,000,000 =
Pre-Calc
Wednesday, November 12, 2008
Section 5.5: Logarithmic Functions
Logarithm of base b of a positive number x:
The exponent when the number is written as a
power of b, where b > 0 and b ≠ 1.
logbx = a if and only if ba = x
NOTE: if no base b is given, assume it is a base of 10
Examples:
log82 = n
log51 = n
log5x = 2
logx64 = 3
Pre-Calc
Wednesday, November 12, 2008
Section 5.5: Logarithmic Functions
Natural Logarithm of a positive number x:
Written as
ln x = logex
ln x = k if and only if ek = x
Examples:
ln x = ½
ln e8 = x
ln
1
e3
=x
Pre-Calc
Wednesday, November 12, 2008