# conversion from dB

#### u-will-neva-no

Joined Mar 22, 2011
230
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)?

#### joeyd999

Joined Jun 6, 2011
4,477
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)?
how about divide by 20 first?

#### Jony130

Joined Feb 17, 2009
5,405
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

#### thatoneguy

Joined Feb 19, 2009
6,359
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
Brilliant, thank you Jony130 and thatoneguy !! 