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Logarithmic Scales - Measured Value (Number) to Magnitude

Level 2

This math topic focuses on logarithmic scales, specifically converting measured values into magnitudes using logarithm functions. It includes problems related to determining magnitudes on the Richter scale from given wave heights and calculating dB (decibel) magnitudes based on sound energy levels. The topic provides advanced exposure to logarithm applications and requires students to understand and solve equations involving logarithms that express physical phenomena like seismic activity and sound intensities.

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

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Logarithmic Scales - Measured Value (Number) to Magnitude Worksheet

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Logarithmic Scales - Measured Value (Number) to Magnitude
1
A LaTex expression showing \text{M} = \log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \text{I} sub 0 = 1\mu \text{m}\\ \text{I} = {6.31 multiplied by 10 to the power of 9 } \mu \text{m}
What is the magnitude on the Richter scale when the wave height is 6.31 x 10^9 micrometers?
a A LaTex expression showing \text{M} = 8.8
b A LaTex expression showing \text{M} = 9.8
2
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 \\ \text{I} = {3.16 multiplied by 10 to the power of -5 } \text{W}/\text{m} to the power of 2
What is the dB magnitude on the decibel scale when the sound energy is 3.16 x 10^-5 W/m^2?
a A LaTex expression showing \beta = 75 \text{dB}
b A LaTex expression showing \beta = 72 \text{dB}
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 \\ \text{I} = {6.31} \text{W}/\text{m} to the power of 2
What is the dB magnitude on the decibel scale when the sound energy is 6.31 W/m^2?
a A LaTex expression showing \beta = 124 \text{dB}
b A LaTex expression showing \beta = 128 \text{dB}
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 \\ \text{I} = {3.98} \text{W}/\text{m} to the power of 2
What is the dB magnitude on the decibel scale when the sound energy is 3.98 W/m^2?
a A LaTex expression showing \beta = 133 \text{dB}
b A LaTex expression showing \beta = 126 \text{dB}
5
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 \\ \text{I} = {1 multiplied by 10 to the power of -10 } \text{W}/\text{m} to the power of 2
What is the dB magnitude on the decibel scale when the sound energy is 1 x 10^-10 W/m^2?
a A LaTex expression showing \beta = 20 \text{dB}
b A LaTex expression showing \beta = 26 \text{dB}
6
A LaTex expression showing \text{M} = \log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \text{I} sub 0 = 1\mu \text{m}\\ \text{I} = {20} \mu \text{m}
What is the magnitude on the Richter scale when the wave height is 20 micrometers?
a A LaTex expression showing \text{M} = 0.3
b A LaTex expression showing \text{M} = 1.3
7
A LaTex expression showing \text{M} = \log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \text{I} sub 0 = 1\mu \text{m}\\ \text{I} = {3.16 multiplied by 10 to the power of 9 } \mu \text{m}
What is the magnitude on the Richter scale when the wave height is 3.16 x 10^9 micrometers?
a A LaTex expression showing \text{M} = 10
b A LaTex expression showing \text{M} = 9.5
8
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 \\ \text{I} = {2 multiplied by 10 to the power of -5 } \text{W}/\text{m} to the power of 2
What is the dB magnitude on the decibel scale when the sound energy is 2 x 10^-5 W/m^2?
a A LaTex expression showing \beta = 73 \text{dB}
b A LaTex expression showing \beta = 80 \text{dB}