How would I solve this Equation?

DB = 10log(I/Io)
DB = 10log (140 Io/Io)
DB = 10 log (140)
DB = ?????

This is as far I have gotten on this equation. Can someone please help me finish? I am trying to determine how many times louder than the threshold of sound is from 140 Decibels.

put this in the google search window:

10*log(140)

It is somewhat less than 22 db

To solve the equation DB = 10log (140), you need to evaluate the logarithm of 140 to the base 10 and then multiply it by 10.

To find the value of log(140) using a scientific calculator or an online calculator:

1. Input 140.
2. Press the "log" button.
3. Press the "=" button.

The calculator should display the value of log(140), which is approximately 2.14612803568.

To multiply the result by 10, simply multiply the value of log(140) by 10, like so:

2.14612803568 * 10 = 21.4612803568

Therefore, DB is approximately equal to 21.4612803568.

To determine how many times louder than the threshold of sound 140 decibels is, you need to understand that the decibel scale is logarithmic.

Assuming the threshold of sound is Io, and DB represents the decibel level, the equation DB = 10log(I/Io) can be rearranged to solve for I/Io:

DB/10 = log(I/Io)

To solve for I/Io, you will need to take the inverse of the logarithm (also called exponentiation) using base 10:

10^(DB/10) = I/Io

Now substitute DB (21.4612803568) into the equation:

10^(21.4612803568/10) = I/Io

Calculating this expression results in approximately 139.9999999999999.

Therefore, sound measured at 140 decibels is approximately 140 times louder than the threshold of sound measured at Io.

To determine the value of DB, let's continue solving the equation step-by-step.

Given:
DB = 10log(I/Io)

In this equation, Io represents the reference intensity, and I represents the actual intensity of the sound.

The next step involves simplifying the expression:

DB = 10log (140 Io/Io)

Since Io/Io = 1 (any number divided by itself equals 1), we can simplify the expression further:

DB = 10 log (140)

Now, we can use a calculator to find the value of log (140):

DB ≈ 10 log (140) ≈ 10 * 2.14612803567

By multiplying 10 and the result of log (140), we find that:

DB ≈ 21.4612803567

Therefore, the value of DB is approximately 21.461 dB after rounding.

Please note that this calculation assumes a base-10 logarithm, which is commonly used in acoustics.