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Logarithmic Scales - Magnitude to Measured Value (Number)

Level 1

This math topic focuses on applying logarithmic functions to practical scenarios involving different scales, such as the pH scale, the decibel scale, and the Richter scale. Students are expected to calculate hydrogen ion concentrations from given pH values, sound intensities from decibel levels, and wave heights from Richter magnitudes. Each problem provides the necessary formulas, requiring students to use logarithmic conversions to find measured values based on given magnitudes.

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 (Number) Worksheet

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Logarithmic Scales - Magnitude to Measured Value (Number)
1
What is the hydrogen ion concentration of a solution with a pH of 8 on the pH scale?
A LaTex expression showing \text{pH} = -\log{[\text{H} to the power of + ]}\\ \\ \text{pH} = 8
a A LaTex expression showing [\text{H} to the power of + ] = {1 multiplied by 10 to the power of -8 } \text{mL}/\text{mol}
b A LaTex expression showing [\text{H} to the power of + ] = {3.16 multiplied by 10 to the power of -7 } \text{mL}/\text{mol}
2
What is the hydrogen ion concentration of a solution with a pH of 6 on the pH scale?
A LaTex expression showing \text{pH} = -\log{[\text{H} to the power of + ]}\\ \\ \text{pH} = 6
a A LaTex expression showing [\text{H} to the power of + ] = {3.16 multiplied by 10 to the power of -5 } \text{mL}/\text{mol}
b A LaTex expression showing [\text{H} to the power of + ] = {1 multiplied by 10 to the power of -6 } \text{mL}/\text{mol}
3
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 + ] = {1 multiplied by 10 to the power of -9 } \text{mL}/\text{mol}
b A LaTex expression showing [\text{H} to the power of + ] = {1 multiplied by 10 to the power of -8 } \text{mL}/\text{mol}
4
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 + ] = {0.1} \text{mL}/\text{mol}
b A LaTex expression showing [\text{H} to the power of + ] = {0.001} \text{mL}/\text{mol}
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 \\ \beta = 20 \text{dB}
What is the sound intensity of a sound with a sound intensity of 20 dB on the decibel scale?
a A LaTex expression showing \text{I} = {1 multiplied by 10 to the power of -8 } \text{W}/\text{m} to the power of 2
b A LaTex expression showing \text{I} = {1 multiplied by 10 to the power of -10 } \text{W}/\text{m} to the power of 2
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 = 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} = {1 multiplied by 10 to the power of -6 } \text{W}/\text{m} to the power of 2
b A LaTex expression showing \text{I} = {1 multiplied by 10 to the power of -5 } \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} = 3
What is the wave height of an earthquake with a magnitude of 3 on the Richter scale?
a A LaTex expression showing \text{I} = {10} \mu \text{m}
b A LaTex expression showing \text{I} = {1,000} \mu \text{m}
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 \\ \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} = {0.0001} \text{W}/\text{m} to the power of 2
b A LaTex expression showing \text{I} = {0.01} \text{W}/\text{m} to the power of 2