Question

Simplify 10 log 2003 without a calculator. Remember that 10 log (2) = 3dB.

Not sure which direction to go. I get 10log2003/log10 or 3dB + 10log(2003/2) when I try to use the hint.

Answer 1

10 log 2003 = 10(log2 + log 1003)
The question is suggesting using the value of 0.3 for log 2, which rounds the actual value to 2 decimal places. Therefore we can use 3.0 for log 1000.
Can you now find the answer?

Answer 2

10 log 2003 = 10(log 2 + log 1003) = 10(0.3 + 3.0) = ?

Answer 3

@optiquest Are you there?

Answer 4

Sorry was working another problem

Answer 5

does 10(log2 + log 1003) = 10(log 2006) ?

Answer 6

Yes you are correct. However if we write:
10(log 2003) = 10(log 2 + log 1001.5)
the right hand side would still become 10(0.3 + 3.0) for the same reason i gave previously.

Answer 7

Oh duh lol

Answer 8

@optiquest Are you cool with the answer now?

Answer 9

Yes thank you

Answer 10

You're welcome :)