# conversion from dB

Discussion in 'Homework Help' started by u-will-neva-no, Jan 11, 2012.

1. ### u-will-neva-no Thread Starter Member

Mar 22, 2011
230
2
Hello everyone,

there should be a relatively easy solution to this but I can't get the correct answer.

$20\log_1_0(x) = 20dB$

How do I find x?

I try to rearrange (taking the exponential of both sides but that does not work). Am I suppost to change the RHS (20dB)?

2. ### joeyd999 AAC Fanatic!

Jun 6, 2011
2,757
2,936
how about divide by 20 first?

3. ### Jony130 AAC Fanatic!

Feb 17, 2009
3,993
1,116
First step

$\frac{20dB}{20} = 1$

Second step

$10^1 = 10$

So the x = 10

for 25dB

$\frac{25dB}{20} = 1.25$

$10^{1.25} = 17.7827941$

u-will-neva-no likes this.
4. ### thatoneguy AAC Fanatic!

Feb 19, 2009
6,357
718
Wiki covers it well

The part where people get caught up is when to use 10 log or 20 log for dB. When measuring voltage or current gain, use 20 log, when measuring power gain, use 10 log.

It is also good to remember the conversion for dB/Octave <-> dB/Decade (left as an exercise for student)

u-will-neva-no likes this.
5. ### u-will-neva-no Thread Starter Member

Mar 22, 2011
230
2
Brilliant, thank you Jony130 and thatoneguy !!