can someone please help me with these college algebra math questions?

Question

use the properities of logarithms to explain how each change affects the scales.

1. how hoes decibel rating of a sound change if its intensity is multiplied by 10?

2. how does richter magnitude of an earthquake change if the energy it releases is multiplied by 10?

3. how does the pH of a substance change if a hydrogen ion concentration is multiplied by 10?

Answer 1

1. Sound intensity:

Reference sound intensity Io = 10^−12 W/m² (Threshold of hearing)

Reference sound intensity level LIo = 0 dB-SIL (Threshold of hearing level)

Get sound intensity I when entering sound intensity level LI:

I = Io×10^(LI/10) W/m² = 10^−12×10^(LI/10) W/m².

Get sound intensity level LI in dB when entering sound intensity I in W/m²

LI = 10×log (I / Io) dB = 10×log (I / 10^−12) dB.

A sound intensity I multiplied by the factor 10 gives a sound intensity level of LI = 10 dB more.

Sound intensity changes with distance after the inverse square law with 1/r².



2. The Richter scale does NOT go from 1 to 10, or between any limits at all. Magnitude 0 and smaller earthquakes happen all the time. An earthquake's Richter magnitude does NOT change with distance from its source.



Question: "The Richter magnitude of an earthquake, M, is related to the energy released in ergs, E, by the formula M=2/3log(E/10^11.8). Find the energy released by an earthquake of magnitude 4.2":

http://openstudy.com/updates/4f62bbb4e4b079c5c6318b14



3. If a hydrogen ion concentration is multiplied by 10 the pH value decreases by 1 pH unit,

e.g. 10^−6 is a pH value of 6 and 10^−6 × 10 = 10^−5, a pH value of 5.



Cheers ebs

Answer 2

Logarithms useful in measuring quantities which

vary widely



Acidity (pH) of a solution

Sound (decibels)

Earthquakes (Richter scale)



Decibels



Suppose I0 is the softest sound the human

ear can hear

measured in watts/cm^2

And I is the watts/cm2 of a given sound



measured in watts/cm2



Then the decibels of the sound is

I

1

0 0log





The log of the

ratio



Logarithms and Orders of

Magnitude



We use the log function because it “counts” the

number of powers of 10

This is necessary because of the vast range of

sound intensity that the human ear can hear



Decibels



If a sound doubles, how many units does its

decibel rating increase?

Answer 3

3. The pH would decrease by 1 pH unit e.g. 10^-7 is a pH of 7 10^-7 x 10 = 10^-6, a pH of 6

Answer 4

I used the definition of a logarithm. LOGaB = X (log with base a to B = x) is corresponding to a^x = b (a raised to the x skill = b) applying this to remedy for C: Q = rx^2c Q/r = x^2c (devide the two sides by r) then applying the def of logarithms: LOGx(Q/r) = 2c and deviding the two sides by 2 c = (a million/2)LOGx(Q/r) This definition continuously tricks me. yet in this, matching the symbols of the definition I gave, x is the equivalent of a, (Q/r) is the equivalent of B and 2c is the equivalent of x.