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Logarithmic Scales - Measured Value (Power) to Magnitude

Level 1

This math topic involves practicing logarithmic functions to compute magnitudes on different scientific scales. Skills honed include determining magnitudes on the Richter scale and decibel scale from given wave heights and sound energy levels, as well as calculating pH values from concentrations of hydrogen ions. Each question presents the necessary logarithmic functions and gives two possible answers, requiring comprehension of logarithms to select the correct value. The problems vary in difficulty and numerical magnitude, preparing learners to handle logarithms in practical scientific measurement contexts.

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

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Logarithmic Scales - Measured Value (Power) to Magnitude Worksheet

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Logarithmic Scales - Measured Value (Power) 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} = 10 to the power of 6 \mu \text{m}
What is the magnitude on the Richter scale when the wave height is 10^6 micrometers?
a A LaTex expression showing \text{M} = 6
b A LaTex expression showing \text{M} = 7
2
A LaTex expression showing \text{pH} = -\log{[\text{H} to the power of + ]}\\ \\ [\text{H} to the power of + ] = 10 to the power of -100,000,000 \text{mL}/\text{mol}
What is the pH on the pH scale when the hydrogen ion concentration is 10^-100,000,000 mL/mol?
a A LaTex expression showing \text{pH} = 8
b A LaTex expression showing \text{pH} = 7.5
3
A LaTex expression showing \text{M} = \log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \text{I} sub 0 = 1\mu \text{m}\\ \text{I} = 10 to the power of 9 \mu \text{m}
What is the magnitude on the Richter scale when the wave height is 10^9 micrometers?
a A LaTex expression showing \text{M} = 9
b A LaTex expression showing \text{M} = 9.5
4
A LaTex expression showing \text{M} = \log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \text{I} sub 0 = 1\mu \text{m}\\ \text{I} = 10 to the power of 4 \mu \text{m}
What is the magnitude on the Richter scale when the wave height is 10^4 micrometers?
a A LaTex expression showing \text{M} = 4
b A LaTex expression showing \text{M} = 4.5
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} = 10 to the power of 38 \text{W}/\text{m} to the power of 2
What is the dB magnitude on the decibel scale when the sound energy is 10^38 W/m^2?
a A LaTex expression showing \beta = 52 \text{dB}
b A LaTex expression showing \beta = 50 \text{dB}
6
What is the pH on the pH scale when the hydrogen ion concentration is 10^-2,147,483,647 mL/mol?
A LaTex expression showing \text{pH} = -\log{[\text{H} to the power of + ]}\\ \\ [\text{H} to the power of + ] = 10 to the power of -2,147,483,647 \text{mL}/\text{mol}
a A LaTex expression showing \text{pH} = 11
b A LaTex expression showing \text{pH} = 9
7
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} = 10 to the power of 58 \text{W}/\text{m} to the power of 2
What is the dB magnitude on the decibel scale when the sound energy is 10^58 W/m^2?
a A LaTex expression showing \beta = 77 \text{dB}
b A LaTex expression showing \beta = 70 \text{dB}
8
A LaTex expression showing \text{M} = \log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \text{I} sub 0 = 1\mu \text{m}\\ \text{I} = 10 to the power of 1 \mu \text{m}
What is the magnitude on the Richter scale when the wave height is 10^1 micrometers?
a A LaTex expression showing \text{M} = 1
b A LaTex expression showing \text{M} = -0.5