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dB
PROBLEMS
SECTION 23.1 Logarithms
1. a. Determine the frequencies (in kHz) at the points indicated
on the plot of Fig. 23.98(a).
b. Determine the voltages (in mV) at the points indicated
on the plot of Fig. 23.98(b).
10 3
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SECTION 23.2 Properties of Logarithms
2. Determine log10 x for each value of x.
a. 100,000 b. 0.0001
c. 10 8
d. 10 �6
e. 20 f. 8643.4
g. 56,000 h. 0.318
3. Given N � log10 x, determine x for each value of N.
a. 3 b. 12
c. 0.2 d. 0.04
e. 10 f. 3.18
g. 1.001 h. 6.1
4. Determine loge x for each value of x.
a. 100,000 b. 0.0001
c. 20 d. 8643.4
Compare with the solutions to Problem 2.
5. Determine log10 48 � log10(8)(6), and compare to
log10 8 � log10 6.
6. Determine log10 0.2 � log10 18/90, and compare to
log10 18 � log10 90.
7. Verify that log10 0.5 is equal to �log10 1/0.5 ��log10 2.
8. Find log10(3) 3 , and compare with 3 log10 3.
SECTION 23.3 Decibels
9. a. Determine the number of bels that relate power levels
of P2 � 280 mW and P1 � 4 mW.
b. Determine the number of decibels for the power levels
of part (a), and compare results.
10. A power level of 100 W is 6 dB above what power level?
(a)
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10 4
( f )
FIG. 23.98
Problem 1.
10 0
10 –1
(b)
(V)
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PROBLEMS ⏐⏐⏐ 1085