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 - Magnitude to Measured Value (Number)

Level 2

This topic focuses on understanding logarithmic scales through practical applications in physics and chemistry. Students learn to convert values on logarithmic scales, such as the decibel scale for sound intensity and the pH scale for hydrogen ion concentration, into measured values or vice versa. The problems cover calculations involving the decibel scale for sound, the pH scale for acidity or basicity of solutions, and presumably other scales like the Richter scale for earthquake magnitude. Advanced logarithm functions are key to solving these conversion tasks, providing real-world relevance to logarithmic calculations in science.

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

more
WorksheetView

Logarithmic Scales - Magnitude to Measured Value (Number) Worksheet

Mobius Math Academy logo
Logarithmic Scales - Magnitude to Measured Value (Number)
1
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 = 71 \text{dB}
What is the sound intensity of a sound with a sound intensity of 71 dB on the decibel scale?
a A LaTex expression showing \text{I} = {1.26 multiplied by 10 to the power of -5 } \text{W}/\text{m} to the power of 2
b A LaTex expression showing \text{I} = {1.26 multiplied by 10 to the power of -7 } \text{W}/\text{m} to the power of 2
2
What is the hydrogen ion concentration of a solution with a pH of 9.7 on the pH scale?
A LaTex expression showing \text{pH} = -\log{[\text{H} to the power of + ]}\\ \\ \text{pH} = 9.7
a A LaTex expression showing [\text{H} to the power of + ] = {2 multiplied by 10 to the power of -10 } \text{mL}/\text{mol}
b A LaTex expression showing [\text{H} to the power of + ] = {6.31 multiplied by 10 to the power of -9 } \text{mL}/\text{mol}
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 \\ \beta = 112 \text{dB}
What is the sound intensity of a sound with a sound intensity of 112 dB on the decibel scale?
a A LaTex expression showing \text{I} = {1.58} \text{W}/\text{m} to the power of 2
b A LaTex expression showing \text{I} = {0.158} \text{W}/\text{m} to the power of 2
4
What is the hydrogen ion concentration of a solution with a pH of 11.9 on the pH scale?
A LaTex expression showing \text{pH} = -\log{[\text{H} to the power of + ]}\\ \\ \text{pH} = 11.9
a A LaTex expression showing [\text{H} to the power of + ] = {3.98 multiplied by 10 to the power of -12 } \text{mL}/\text{mol}
b A LaTex expression showing [\text{H} to the power of + ] = {1.26 multiplied by 10 to the power of -12 } \text{mL}/\text{mol}
5
A LaTex expression showing \text{M} = \log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \text{I} sub 0 = 1\mu \text{m}\\ \text{M} = 4.5
What is the wave height of an earthquake with a magnitude of 4.5 on the Richter scale?
a A LaTex expression showing \text{I} = {31,623} \mu \text{m}
b A LaTex expression showing \text{I} = {3,162,278} \mu \text{m}
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 = 128 \text{dB}
What is the sound intensity of a sound with a sound intensity of 128 dB on the decibel scale?
a A LaTex expression showing \text{I} = {6.31} \text{W}/\text{m} to the power of 2
b A LaTex expression showing \text{I} = {631} \text{W}/\text{m} to the power of 2
7
What is the hydrogen ion concentration of a solution with a pH of 13.8 on the pH scale?
A LaTex expression showing \text{pH} = -\log{[\text{H} to the power of + ]}\\ \\ \text{pH} = 13.8
a A LaTex expression showing [\text{H} to the power of + ] = {1.58 multiplied by 10 to the power of -14 } \text{mL}/\text{mol}
b A LaTex expression showing [\text{H} to the power of + ] = {1.58 multiplied by 10 to the power of -15 } \text{mL}/\text{mol}
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 = 95 \text{dB}
What is the sound intensity of a sound with a sound intensity of 95 dB on the decibel scale?
a A LaTex expression showing \text{I} = {0.00316} \text{W}/\text{m} to the power of 2
b A LaTex expression showing \text{I} = {0.316} \text{W}/\text{m} to the power of 2