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Logarithmic Scales - Measured Value Ratio to Magnitude Difference

Level 1

This math topic involves understanding logarithmic scales and their application in various contexts such as decibels for sound intensity, pH for hydrogen ion concentration, and the Richter scale for earthquake magnitudes. Students practice calculating the differences in logarithmic measurements given different ratios of measured values, focusing on interpreting and computing logarithmic differences based on formulaic expressions for specific real-world scenarios like sound energy differences, hydrogen ion concentration variations, and earthquake wave size comparisons.

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

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Logarithmic Scales - Measured Value Ratio to Magnitude Difference Worksheet

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Logarithmic Scales - Measured Value Ratio to Magnitude Difference
1
A LaTex expression showing \text{dB} = 10\log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \\ \frac{\text{I} sub 2 }{\text{I} sub 1 } = 10
If a sound has 10 times the sound energy as another what is their difference on the decibel scale?
a A LaTex expression showing \beta sub 2 - \beta sub 1 = 10
b A LaTex expression showing \beta sub 2 - \beta sub 1 = 11
2
A LaTex expression showing \text{pH} = -\log{[\text{H} to the power of + ]}\\ \\ \frac{[\text{H} to the power of + ] sub 2 }{[\text{H} to the power of + ] sub 1 } = 100
If a solution has 100 times the Hydrogen ion concentration as another what is their difference on the pH scale?
a A LaTex expression showing \text{pH} sub 2 - \text{pH} sub 1 = -2
b A LaTex expression showing \text{pH} sub 2 - \text{pH} sub 1 = -3
3
A LaTex expression showing \text{dB} = 10\log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \\ \frac{\text{I} sub 2 }{\text{I} sub 1 } = 100,000
If a sound has 100,000 times the sound energy as another what is their difference on the decibel scale?
a A LaTex expression showing \beta sub 2 - \beta sub 1 = 48
b A LaTex expression showing \beta sub 2 - \beta sub 1 = 50
4
A LaTex expression showing \text{M} = \log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \\ \frac{\text{I} sub 2 }{\text{I} sub 1 } = 100
If an earthquake has 100 times the wave size as another what is their difference on the Richter scale?
a A LaTex expression showing \text{M} sub 2 - \text{M} sub 1 = 4
b A LaTex expression showing \text{M} sub 2 - \text{M} sub 1 = 2
5
A LaTex expression showing \text{M} = \log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \\ \frac{\text{I} sub 2 }{\text{I} sub 1 } = 10,000
If an earthquake has 10,000 times the wave size as another what is their difference on the Richter scale?
a A LaTex expression showing \text{M} sub 2 - \text{M} sub 1 = 4
b A LaTex expression showing \text{M} sub 2 - \text{M} sub 1 = 5
6
A LaTex expression showing \text{M} = \log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \\ \frac{\text{I} sub 2 }{\text{I} sub 1 } = 1 multiplied by 10 to the power of 8
If an earthquake has 1 x 10^8 times the wave size as another what is their difference on the Richter scale?
a A LaTex expression showing \text{M} sub 2 - \text{M} sub 1 = 7.5
b A LaTex expression showing \text{M} sub 2 - \text{M} sub 1 = 8
7
A LaTex expression showing \text{M} = \log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \\ \frac{\text{I} sub 2 }{\text{I} sub 1 } = 1,000,000
If an earthquake has 1,000,000 times the wave size as another what is their difference on the Richter scale?
a A LaTex expression showing \text{M} sub 2 - \text{M} sub 1 = 8
b A LaTex expression showing \text{M} sub 2 - \text{M} sub 1 = 6
8
A LaTex expression showing \text{M} = \log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \\ \frac{\text{I} sub 2 }{\text{I} sub 1 } = 10
If an earthquake has 10 times the wave size as another what is their difference on the Richter scale?
a A LaTex expression showing \text{M} sub 2 - \text{M} sub 1 = 1
b A LaTex expression showing \text{M} sub 2 - \text{M} sub 1 = -0.5