How to add Decibels? I have just started studying Audio Engineering and I have come across a section where I need to add decibel levels together. I am aware that adding two decibel levels together will always give you the answer of +3dB (e.g, 90dB + 90dB = 93dB) However, the equation I am using to do this is; $$\log_{10}\left( 10^{90/10}+10^{90/10}\right).$$ The answer that this gives me is "2,000,000,000" Is there a step that I am missing here? Thanks!

Decibels do not add. What we add is the power (assuming no interference). See the wikipedia page to know how decibels are related to powers. <

$$dB=10\lg P.$$

So if power $P=1$, we have $dB=0$. And if $P=10$, we have $dB=10$. A similarly defined quantity in chemistry is $pH$, which is related to the base-$10$ log (i.e., $\lg$) of the $H^+$ concentration. So to add two decibels, just convert them to powers first, add the powers and then convert back. For $90$ dB, the corresponding $P=10^9$. Adding two $10^9$ gives $2\times 10^9$. Then take the log and multiply by $10$ to get $93$ dB. What you're missing is converting the power back to $dB$.