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 - Ratio and Magnitude to Magnitude

Level 1

This topic focuses on understanding logarithmic scales across various scientific and mathematical contexts. It involves problems that require conversion between ratios and magnitudes, particularly in measuring pH levels, earthquake magnitudes on the Richter scale, and decibel (dB) sound levels. Each problem presents a scenario asking to calculate the new scale measurement after a specified change in ratio (e.g., an increase in hydrogen ion concentration or sound energy). The skill practiced is the application of logarithmic equations to solve real-world problems in different scales, enhancing the understanding of logarithmic relationships and their practical implications.

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

more
WorksheetView

Logarithmic Scales - Ratio and Magnitude to Magnitude Worksheet

Mobius Math Academy logo
Logarithmic Scales - Ratio and Magnitude to Magnitude
1
A LaTex expression showing \text{pH} = -\log{[\text{H} to the power of + ]}\\ \\ \frac{[\text{H} to the power of + ] sub 2 }{[\text{H} to the power of + ] sub 1 } = 1 multiplied by 10 to the power of 9 \\ \text{pH} sub 1 = 10
If a solution has 1 x 10^9 times the Hydrogen ion concentration as one with a pH of 10 on the pH scale, what is it's pH?
a A LaTex expression showing \text{pH} sub 2 = 2.5
b A LaTex expression showing \text{pH} sub 2 = 1
2
A LaTex expression showing \text{M} = \log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \\ \frac{\text{I} sub 2 }{\text{I} sub 1 } = 1,000 \\ \text{M} sub 1 = 3
If an earthquake has 1,000 times the wave size as one with a magnitude of 3 on the Richter scale, what is it's magnitude?
a A LaTex expression showing \text{M} sub 2 = 6.5
b A LaTex expression showing \text{M} sub 2 = 6
3
A LaTex expression showing \text{pH} = -\log{[\text{H} to the power of + ]}\\ \\ \frac{[\text{H} to the power of + ] sub 2 }{[\text{H} to the power of + ] sub 1 } = 10 \\ \text{pH} sub 1 = 10
If a solution has 10 times the Hydrogen ion concentration as one with a pH of 10 on the pH scale, what is it's pH?
a A LaTex expression showing \text{pH} sub 2 = 11
b A LaTex expression showing \text{pH} sub 2 = 9
4
A LaTex expression showing \text{dB} = 10\log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \\ \frac{\text{I} sub 2 }{\text{I} sub 1 } = 1 multiplied by 10 to the power of 11 \\ \beta sub 1 = 20 \text{dB}
If a sound has 1 x 10^11 times the sound energy as one with a dB magnitude of 20 on the decibel scale, what is it's dB magnitude?
a A LaTex expression showing \beta sub 2 = 135 \text{dB}
b A LaTex expression showing \beta sub 2 = 130 \text{dB}
5
A LaTex expression showing \text{dB} = 10\log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \\ \frac{\text{I} sub 2 }{\text{I} sub 1 } = 10 \\ \beta sub 1 = 110 \text{dB}
If a sound has 10 times the sound energy as one with a dB magnitude of 110 on the decibel scale, what is it's dB magnitude?
a A LaTex expression showing \beta sub 2 = 120 \text{dB}
b A LaTex expression showing \beta sub 2 = 114 \text{dB}
6
A LaTex expression showing \text{pH} = -\log{[\text{H} to the power of + ]}\\ \\ \frac{[\text{H} to the power of + ] sub 2 }{[\text{H} to the power of + ] sub 1 } = 1 multiplied by 10 to the power of 9 \\ \text{pH} sub 1 = 11
If a solution has 1 x 10^9 times the Hydrogen ion concentration as one with a pH of 11 on the pH scale, what is it's pH?
a A LaTex expression showing \text{pH} sub 2 = 2
b A LaTex expression showing \text{pH} sub 2 = 0.5
7
A LaTex expression showing \text{M} = \log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \\ \frac{\text{I} sub 2 }{\text{I} sub 1 } = 100 \\ \text{M} sub 1 = 7
If an earthquake has 100 times the wave size as one with a magnitude of 7 on the Richter scale, what is it's magnitude?
a A LaTex expression showing \text{M} sub 2 = 9
b A LaTex expression showing \text{M} sub 2 = 10.5
8
A LaTex expression showing \text{pH} = -\log{[\text{H} to the power of + ]}\\ \\ \frac{[\text{H} to the power of + ] sub 2 }{[\text{H} to the power of + ] sub 1 } = 100,000 \\ \text{pH} sub 1 = 12
If a solution has 100,000 times the Hydrogen ion concentration as one with a pH of 12 on the pH scale, what is it's pH?
a A LaTex expression showing \text{pH} sub 2 = 7
b A LaTex expression showing \text{pH} sub 2 = 7.5