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### Solving a Decibel Noise Equation

```
Date: 05/23/2000 at 17:58:23
From: Ian Hazelden
Subject: Noise Equations

How do you rearrange the formula 50 = 94.5 - 20log(r) - 8 to solve for
r?
```

```
Date: 05/23/2000 at 18:04:13
From: Doctor Douglas
Subject: Re: Noise Equations

Hi Ian,

Thanks for sending your question to Ask Dr. Math. Since you write
"noise" equations in the subject line, I presume that you are talking
about sound intensity and that the logarithm is the appropriate one
for decibels (it is the log base 10.) With that, we rearrange the
formula that you gave:

50 = 94.5 - 20 log(r) - 8

20 log(r) = 94.5 - 8 - 50

20 log(r) = 36.5

log(r) = 36.5 / 20

= 1.825

Now raise ten (it could be any number, but we are choosing to use log
base 10) to both sides:

log(r)     1.825
10       = 10

1.825
r   = 10

= 66.83

- Doctor Douglas, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Logs
High School Physics/Chemistry

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