How Do Decibels Determine Perceived Loudness and Amplifier Gain?

[leospyder]

Can someone help me with the following questions (I have no idea where to begin in either case). There are no questions that follow these same types of concepts in the book problems.

1) A 6000 Hz tone must have what sound level to seem as loud as a 100
Hz tone that has a 50 dB sound level?

2) In audio and communications systems, the gain, denoted by b, in
decibels is defined as

$$\beta = (P_{out}/P_{in})$$

where $$P_{in}$$ is the power input and $$P_{out}$$
is the power output. Assume a particular stereo amplifier will put out 150 W of
power for an input of 1 mW. What is its gain in dB?

 

[pseudovector]

1)http://www.phys.unsw.edu.au/~jw/dB.html
look at the chart under "Loudness, phons and sones". All the dots on any curve are combinations of frequency with corresponding intensity have the same loudness. So you need to find on which curve (100Hz, 50dB) is, and see where the 6000Hz line intersects that curve.
2) Just divide the output power by the input power