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Logarithmic measurement scales
Logarithmic measurement scales
Example 1
A logarithmic magnitude scale is M=log10(I0I). One event has magnitude 3, another 8. How many times as intense is the second?
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Answer: 100000
- Subtracting magnitudes gives log10(I1I2)=5. Thus I1I2=105=100000.
Example 2
Sound level is L=10log10(I0I) dB. Intensity increases by factor 100000. By how many decibels does L increase?
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Answer: 50
- Change in L=10log10(100000)=10×5=50 dB.
Example 3
pH=−log10(H), where H is the hydrogen-ion concentration in Lmol. If H=10−7, find pH.
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Answer: 7
- log10(10−7)=−7; taking its negative gives pH=7.
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