# Why does base 10 log is best for finding gain in decibel?

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#### electronics_kumar GAIN CALCULATIONS

FOR FINDING GAIN IN DECIBEL ,IT ALWAYS " BASE 10 LOG" IS RECOMMENDED..WHY IT IS SO ..WHY NO ROOM FOR BASE EXP. LOG" FOR IT..IS THERE ANY SPECIAL ADVANTAGE OF HAVING IT

#### v_c Re: GAIN CALCULATIONS

that is by definition. The ratio of voltages use 20 log() and ratio of powers uses 10 log(). Everything you want to know and more is here https://en.wikipedia.org/wiki/Decibel

One note the "B" in "dB" is always capitalized because it stands for the name of the person that this unit was named after -- Bell (Alexander Graham Bell).

Best regards,
v_c

#### eda_freak

##### Member level 3 Re: GAIN CALCULATIONS

(10)*x=y
x log (10)= log so if log is to base 10
we have x= log to base 10....
now number system we use is decimal so when we have x which is infact the power of 10 that gives value equal to y...calculations become easier...
i hope that explains it...

#### pks

##### Newbie level 2 Re: GAIN CALCULATIONS

During gain calculations we use log10 because. Gain is related to the ratio of output power to the input power. This power ratio is expressed in bels . A basic unit for power ratio. The decibel (dB) which is 1/10 of bell is derived from it. that is the reason why we use dB. Also exponentioal powers are unconventional for our day to day calculations. so power raised to 10 is very conveneient.

#### lokeyh Re: GAIN CALCULATIONS

Using log will compress the plot. When we want to plot a frequency response that varies from 1000 to 1, it will easier to plot 20log(1000)=60 to 20log(1)=0 as the scale is smaller.

#### sivani_vs

##### Junior Member level 3 Re: GAIN CALCULATIONS

The only advantage of using log 10 is that to compress the scale than log e.

#### dreamcard

##### Member level 2 GAIN CALCULATIONS

the range is wider in decibel definition

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