Home
Grade 1Grade 2Grade 3Grade 4Grade 5Grade 6Grade 7Grade 8Grade 9Grade 10Grade 11Grade 12Math Themes
Explorers (Grades 1-3)Explorers Elite (1-3)Navigators (Grades 4-6)Navigators Elite (4-6)Challengers (Grades 7-9)Challengers Elite (7-9)Scholars (Grades 10-12)Scholars Elite (10-12)Schedule an Evaluation
Mobius MethodFlexible ClassesCompanySupport
Pricing
Ctrl+k
Sign InJoin

Logarithmic Scales - Measured Value (Power) to Magnitude

Level 2

This math topic focuses on logarithmic scales related to measured values and their magnitudes. Students learn to calculate the magnitude on the Richter scale given specific wave heights and to find the pH value from given hydrogen ion concentrations. The topic includes advanced logarithm functions, emphasizing the practical application of logarithms in real-world scientific measurements such as seismic activity and acidity levels.

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

more
WorksheetView

Logarithmic Scales - Measured Value (Power) to Magnitude Worksheet

Mobius Math Academy logo
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 2.5 \mu \text{m}
What is the magnitude on the Richter scale when the wave height is 10^2.5 micrometers?
a A LaTex expression showing \text{M} = 1.5
b A LaTex expression showing \text{M} = 2.5
2
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 8.1 \mu \text{m}
What is the magnitude on the Richter scale when the wave height is 10^8.1 micrometers?
a A LaTex expression showing \text{M} = 7.6
b A LaTex expression showing \text{M} = 8.1
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 4.6 \mu \text{m}
What is the magnitude on the Richter scale when the wave height is 10^4.6 micrometers?
a A LaTex expression showing \text{M} = 4.6
b A LaTex expression showing \text{M} = 4.1
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 6.2 \mu \text{m}
What is the magnitude on the Richter scale when the wave height is 10^6.2 micrometers?
a A LaTex expression showing \text{M} = 6.2
b A LaTex expression showing \text{M} = 4.2
5
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 6.8 \mu \text{m}
What is the magnitude on the Richter scale when the wave height is 10^6.8 micrometers?
a A LaTex expression showing \text{M} = 7.8
b A LaTex expression showing \text{M} = 6.8
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} = 12.9
b A LaTex expression showing \text{pH} = 13.4
7
A LaTex expression showing \text{pH} = -\log{[\text{H} to the power of + ]}\\ \\ [\text{H} to the power of + ] = 10 to the power of -501 \text{mL}/\text{mol}
What is the pH on the pH scale when the hydrogen ion concentration is 10^-501 mL/mol?
a A LaTex expression showing \text{pH} = 2.7
b A LaTex expression showing \text{pH} = 4.7
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} = 10 to the power of 47 \text{W}/\text{m} to the power of 2
What is the dB magnitude on the decibel scale when the sound energy is 10^47 W/m^2?
a A LaTex expression showing \beta = 61 \text{dB}
b A LaTex expression showing \beta = 59 \text{dB}