Precal Blog

Now that my computer is virus free, i can post my blog on logarithms.

So the past few days we’ve spent time using logarithms to find things like magnitudes and decibels. We’ve come to defining the logarithm as the exponent raised to a power of 10. For example:

log(100)=2 because 10^2=100

We’ve learned to find Magnitude of an earthquake as log(I/Io). (I/Io) is the relative intensity. That means you take the value for which you want to find the magnitude of over the smallest detectable earthquake which is given. Io= 2.00 x 10^11 in any case that deals with magnitude. Let’s say I= 2.518 x 10^18. We would have:

log(2.518 x 10^18/2.00 x 10^11). When you divide these values, you get an exponent of 7. Since the number you get isn’t a power of 10 raised to an integer, the log won’t be an integer. It is actually 7.1

We also got the problem:

How many times more powerful is the sound of a chainsaw (110dB) than the noise generated by a vaccum cleaner (sound intensity 10^-2)

We have to find the sound intensity of the chainsaw. In order to do this, we need the equation for dB

dB= 10*log(I/Io) Io= 10^-12. This is the smallest detectable sound by the human ear.

110=10*log(I/10^-12)

11=log(I/10^-12)

Since our answer is 11, we know that  the number inside the parenthesis will have a power of 11. We know the rule for dividing exponents is that you subtract them so x–12=11. x=-1

11=log(10^-1/10^-12)

The relative intensity for a chainsaw is 10^11

The relative intensity for a vacuum cleaner is (10^-2/10^-12)= 10^10

So we see that a chainsaw’s sound is 10 times more powerful than that of  a vacuum cleaner.

That’s it for logs- the next scribe izzz Steeenz Lyrixz AKA Eric