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Logarithmic Scales - Magnitude to Measured Value (Power)

Level 1

This math topic focuses on understanding and applying logarithmic scales related to real-world phenomena. It covers computations using the Richter scale for earthquake wave heights, the decibel scale for sound intensity, and the pH scale for hydrogen ion concentration. Problems require converting magnitudes to measured values using logarithmic relationships, specifically addressing how to determine values from a given logarithmic scale (e.g., finding wave heights from earthquake magnitudes or sound intensities from decibel levels).

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Logarithmic Scales - Magnitude to Measured Value (Power) Worksheet

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Logarithmic Scales - Magnitude to Measured Value (Power)
1
A LaTex expression showing \text{M} = \log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \text{I} sub 0 = 1\mu \text{m}\\ \text{M} = 5
What is the wave height of an earthquake with a magnitude of 5 on the Richter scale?
a A LaTex expression showing \text{I} = 10 to the power of 5 \mu \text{m}
b A LaTex expression showing \text{I} = 10 to the power of 4 \mu \text{m}
2
A LaTex expression showing \text{M} = \log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \text{I} sub 0 = 1\mu \text{m}\\ \text{M} = 9
What is the wave height of an earthquake with a magnitude of 9 on the Richter scale?
a A LaTex expression showing \text{I} = 10 to the power of 9 \mu \text{m}
b A LaTex expression showing \text{I} = 10 to the power of 11 \mu \text{m}
3
A LaTex expression showing \text{dB} = 10\log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \text{I} sub 0 = 10 to the power of -12 \text{W}/\text{m} to the power of 2 \\ \beta = 60 \text{dB}
What is the sound intensity of a sound with a sound intensity of 60 dB on the decibel scale?
a A LaTex expression showing \text{I} = 10 to the power of 48 \text{W}/\text{m} to the power of 2
b A LaTex expression showing \text{I} = 10 to the power of 58 \text{W}/\text{m} to the power of 2
4
A LaTex expression showing \text{dB} = 10\log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \text{I} sub 0 = 10 to the power of -12 \text{W}/\text{m} to the power of 2 \\ \beta = 120 \text{dB}
What is the sound intensity of a sound with a sound intensity of 120 dB on the decibel scale?
a A LaTex expression showing \text{I} = 10 to the power of 108 \text{W}/\text{m} to the power of 2
b A LaTex expression showing \text{I} = 10 to the power of 118 \text{W}/\text{m} to the power of 2
5
A LaTex expression showing \text{M} = \log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \text{I} sub 0 = 1\mu \text{m}\\ \text{M} = 4
What is the wave height of an earthquake with a magnitude of 4 on the Richter scale?
a A LaTex expression showing \text{I} = 10 to the power of 4 \mu \text{m}
b A LaTex expression showing \text{I} = 10 to the power of 3.5 \mu \text{m}
6
A LaTex expression showing \text{dB} = 10\log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \text{I} sub 0 = 10 to the power of -12 \text{W}/\text{m} to the power of 2 \\ \beta = 110 \text{dB}
What is the sound intensity of a sound with a sound intensity of 110 dB on the decibel scale?
a A LaTex expression showing \text{I} = 10 to the power of 93 \text{W}/\text{m} to the power of 2
b A LaTex expression showing \text{I} = 10 to the power of 98 \text{W}/\text{m} to the power of 2
7
What is the hydrogen ion concentration of a solution with a pH of 1 on the pH scale?
A LaTex expression showing \text{pH} = -\log{[\text{H} to the power of + ]}\\ \\ \text{pH} = 1
a A LaTex expression showing [\text{H} to the power of + ] = 10 to the power of -100 \text{mL}/\text{mol}
b A LaTex expression showing [\text{H} to the power of + ] = 10 to the power of -10 \text{mL}/\text{mol}
8
What is the hydrogen ion concentration of a solution with a pH of 9 on the pH scale?
A LaTex expression showing \text{pH} = -\log{[\text{H} to the power of + ]}\\ \\ \text{pH} = 9
a A LaTex expression showing [\text{H} to the power of + ] = 10 to the power of -1,000,000,000 \text{mL}/\text{mol}
b A LaTex expression showing [\text{H} to the power of + ] = 10 to the power of -316,227,766 \text{mL}/\text{mol}