Logarithm is in everyday life. Basically this subtopic is just about applying logarithm into pH value, Decibel Scale and Ritcher Scale. It's important for us to memorize three important formulas in this subtopic.
1. pH = - log [ H+] , where H+ is the concentration of hydronium ions in moles/litre
Example: pH = - log (10-4) = - (-4) = +4
Therefor, the pH value for this solution is Acidic.
It's also important for you to know the pH scale! Don't mixed up with acidic and alkaline.
Refer to the diagram above if you are not so sure about pH scale.
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2. β 2 – β 1 = 10 log (I1 / I2) , where β 2 – β 1 is the difference in sound level, in decibels, and (I1 / I2) is the ratio of their sound intensities, where I is measured in watts per square metre (W/m2).
We need to be sure about the Decibel Scale too. Here i found you the scale of different sounds.
3. Ritcher Scale: M = log (I / I0), where M is the magnitude of earthquake, I is the intensity of earthquake and I0 is the intensity of standard earthquake.
A fun fact to share: In 1935 Charles Richter defined the magnitude of an earthquake to be
,where I is the intensity of the earthquake (measured by the amplitude of a seismograph reading taken 100 km from the epicenter of the earthquake) and S is the intensity of a ''standard earthquake'' (whose amplitude is 1 micron =10-4 cm).
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When we are doing this subtopic, we used to see question comparing magnitude or dB and intensity of both Decibel Scale and Ritcher Scale. Please always remember that Comparing magnitude or dB and intensity are different! So, do not mixed up!
There are not much videos on the Internet. This is a video that i found it relevant to Logarithmic Scales in the Physical Sciences.
Source: AlRichards314, Youtube, 10 May 2009.
S.O.S. Math, "Application of Exponential and Logarithmic Function", 1999
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