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## Homework Statement

The sound at a concert is measured to be 0.5 W/m^2. How many decibels is this?

## Homework Equations

β = 10ln(I/I_0)

I/I_0 = 10^(β/10)

## The Attempt at a Solution

I_0 = 1*10^-12 W/m^2

I = 0.5 W/m^2

Therefore,

β = 10ln(0.5/10^-12)

β = 269.378 dB

However,

.5/10^12 = 10^(β/10)

When using a TI-89 calculator to solve for β the answer comes to 116.99 dB, what I expected.

I can't find anything wrong with my work, but the dB level seems way too high for the first equation. I expected it should be somewhere around 115 dB. Why does the formula involving natural logs give the wrong answer?