## Transcribed Text

Please post your calculations (show your work!)
1. antilog10 301 =
[Hint: antilog is the reverse function of a log, or 10*]
2. antilog10 1.301 -
[Hint: use the exponents law: log ax X log as = log ax+y
Now, using log10 2 .3, calculate the following without using a
calculator or log table.
3. log10 20 =
4. log10 (2) =
5. log10 8 =
Please post your observations:
1. What is most challenging about this exercise?
2. Any realizations resulting from going through this process?
3. Does anything remain confusing to you about working with logs
and antilogs or exponents?
4. Are there any additional insights that you can share with your
fellow classmates to help solidify these concepts?
For your final assignment this week, you will work out the following problems. Please
show all your work. No credit will be given for incomplete answers.
Using log10 2 3, solve the following without using a calculator or log table. Please show your
work!
1. log10 40
=
2. log1o
(4)
3. log1o 16 =
The signal-to-noise ratio of a digital audio system can be derived from the following formula:
SNRdB 20 log 2n [n number of bits per sample]
4. Simplify this expression to show that the signal to noise ratio can be expressed as 6n.
Electrical power can be expressed in decibels using the following formula:
PdB 10 log1o
(i)
[P, Pret power (watts)]
5. If Prof .001 watts, what is the power in dB when P = watt?
The output of an audio amplifier can be compared to its input using the following formula:
(Vout
AVdE 20 log1o Vin / (Vour Vin = voltage (volts), AV change in voltage]
6. Show that AV is always equal to 6 dB if the output is twice the voltage of the input.
Using our decibel equations and a scientific calculator when necessary, solve the following.
Please show your work!
7. The input to an audio amplifier is known to be 2.5 watts, and the output is 25 watts. What is the
gain of the amplifier in dB?
8. The output of an amplifier is half the power of the input. Express the output in dB, relative to the
input.
9. How much voltage would appear at the output of a compressor indicating 7 dB gain reduction, if
the input was 1.22 volts?
10. An audio signal passes through two devices, each doubling its input voltage. What is the gain of
the entire system, in dB?
EXTRA CREDIT
Two audio devices are placed in series such that:
Vlout
GF 20 log Vlin [G1 gain of device one]
V2out
G2=
20 log V2in [G2= gain of device two]
Show that
G3= G++ G2, [G3= gain of device one and device two in series].
Hint: use the rule for expressing the log of a product as the sum of two logs.)

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