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Logarithmic Scales - Magnitude to Measured Value (Power)

Level 2

This math topic focuses on applying logarithmic scales to practical examples involving sound intensity, hydrogen ion concentrations, and earthquake wave heights. It covers: 1. Calculating sound intensities using the decibel scale, given dB levels. 2. Determining hydrogen ion concentrations from given pH values using the negative logarithm function. 3. Estimating wave heights of earthquakes from magnitudes on the Richter scale. These problems require understanding of logarithmic relationships and the ability to convert logarithmic forms into measured values in various scientific contexts.

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{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 = 80 \text{dB}
What is the sound intensity of a sound with a sound intensity of 80 dB on the decibel scale?
a A LaTex expression showing \text{I} = 10 to the power of 73 \text{W}/\text{m} to the power of 2
b A LaTex expression showing \text{I} = 10 to the power of 68 \text{W}/\text{m} to the power of 2
2
What is the hydrogen ion concentration of a solution with a pH of 4.7 on the pH scale?
A LaTex expression showing \text{pH} = -\log{[\text{H} to the power of + ]}\\ \\ \text{pH} = 4.7
a A LaTex expression showing [\text{H} to the power of + ] = 10 to the power of -50,118 \text{mL}/\text{mol}
b A LaTex expression showing [\text{H} to the power of + ] = 10 to the power of -5,011,872 \text{mL}/\text{mol}
3
A LaTex expression showing \text{M} = \log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \text{I} sub 0 = 1\mu \text{m}\\ \text{M} = 2
What is the wave height of an earthquake with a magnitude of 2 on the Richter scale?
a A LaTex expression showing \text{I} = 10 to the power of 0.5 \mu \text{m}
b A LaTex expression showing \text{I} = 10 to the power of 2 \mu \text{m}
4
What is the hydrogen ion concentration of a solution with a pH of 5.5 on the pH scale?
A LaTex expression showing \text{pH} = -\log{[\text{H} to the power of + ]}\\ \\ \text{pH} = 5.5
a A LaTex expression showing [\text{H} to the power of + ] = 10 to the power of -316,227 \text{mL}/\text{mol}
b A LaTex expression showing [\text{H} to the power of + ] = 10 to the power of -3,162 \text{mL}/\text{mol}
5
What is the hydrogen ion concentration of a solution with a pH of 5 on the pH scale?
A LaTex expression showing \text{pH} = -\log{[\text{H} to the power of + ]}\\ \\ \text{pH} = 5
a A LaTex expression showing [\text{H} to the power of + ] = 10 to the power of -10,000,000 \text{mL}/\text{mol}
b A LaTex expression showing [\text{H} to the power of + ] = 10 to the power of -100,000 \text{mL}/\text{mol}
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 = 101 \text{dB}
What is the sound intensity of a sound with a sound intensity of 101 dB on the decibel scale?
a A LaTex expression showing \text{I} = 10 to the power of 94 \text{W}/\text{m} to the power of 2
b A LaTex expression showing \text{I} = 10 to the power of 89 \text{W}/\text{m} to the power of 2
7
A LaTex expression showing \text{M} = \log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \text{I} sub 0 = 1\mu \text{m}\\ \text{M} = 6.9
What is the wave height of an earthquake with a magnitude of 6.9 on the Richter scale?
a A LaTex expression showing \text{I} = 10 to the power of 8.9 \mu \text{m}
b A LaTex expression showing \text{I} = 10 to the power of 6.9 \mu \text{m}
8
A LaTex expression showing \text{M} = \log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \text{I} sub 0 = 1\mu \text{m}\\ \text{M} = 9.6
What is the wave height of an earthquake with a magnitude of 9.6 on the Richter scale?
a A LaTex expression showing \text{I} = 10 to the power of 9.6 \mu \text{m}
b A LaTex expression showing \text{I} = 10 to the power of 8.1 \mu \text{m}