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dB
(23.6)
5. The log of a number taken to a power is equal to the product of
the power and the log of the number.
Calculator Functions
log 10 � a
b � � log 10 a � log 10 b
log 10 a n � n log 10 a
(23.7)
On most calculators the log of a number is found by simply entering the
number and pressing the
For example,
or key.
log10 80 �
with a display of 1.903.
For the reverse process, where N, or the antilogarithm, is desired, the
function 10 x is employed. On most calculators 10 x LOG IN
8 0 LOG
appears as a second
function above the LOG key. For the case of
0.6 � log10 N
the following keys are employed:
2ND F
with a display of 3.981. Checking: log 10 3.981 � 0.6.
6
EXAMPLE 23.2 Evaluate each of the following logarithmic expressions:
a. log10 0.004
b. log10 250,000
c. log10(0.08)(240) 1 � 10
d. log10 4
���4
1 � 10
e. log10(10) 4
Solutions:
a. �2.398
b. �5.398
c. log 10(0.08)(240) � log 10 0.08 � log 10 240 � �1.097 � 2.380
� 1.283
d. log10 � log10 1 � 10 4 � log10 1 � 10 �4 � 4 � (�4)
� 8
e. log10 10 4 1 � 10
� 4 log10 10 � 4(1) � 4
4
���4
1 � 10
23.3 DECIBELS
Power Gain
Two levels of power can be compared using a unit of measure called the
bel, which is defined by the following equation:
10 x
DECIBELS ⏐⏐⏐ 1021