The speaker at the concert has the sound intensity level of 100 dB if we listen from the distance 5 m. How far from the speaker does the intensity level drop to the safe value of 85 dB?

far from the speaker the intensity drops to 85 dB.

Explanation:

In the equation for the Decibel scale

The ratio of the intensities can be written as

And since

and

,

meaning

Putting this into equation (1), we get:

Now, if the intensity is 100 dB when the distance is 5 meters, we have:

by taking both sides to the exponent:  

Now equation (2) becomes

when the intensity level is 85 dB we have

take both sides to exponents and we get:

Thus, far from the speaker the intensity drops to 85 dB.