Logarithmic Scales - Magnitude Difference to Measured Value Ratio (Level 1)

Logarithmic Scales - Magnitude Difference to Measured Value Ratio

$A LaTex expression showing \text{pH} = -\log{[\text{H} to the power of + ]}\\ \\ \text{pH} sub 2 - \text{pH} sub 1 = -3$

If a solution has a pH 3 lower on the pH scale what is the ratio of their Hydrogen ion concentration measurements?

a $A LaTex expression showing \frac{[\text{H} to the power of + ] sub 2 }{[\text{H} to the power of + ] sub 1 } = 31,623$

b $A LaTex expression showing \frac{[\text{H} to the power of + ] sub 2 }{[\text{H} to the power of + ] sub 1 } = 1,000$

$A LaTex expression showing \text{M} = \log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \\ \text{M} sub 2 - \text{M} sub 1 = 3$

If an earthquake has a magnitude 3 higher on the Richter scale what is the ratio of their wave size measurements?

a $A LaTex expression showing \frac{\text{I} sub 2 }{\text{I} sub 1 } = 31,623$

b $A LaTex expression showing \frac{\text{I} sub 2 }{\text{I} sub 1 } = 1,000$

$A LaTex expression showing \text{dB} = 10\log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \\ \beta sub 2 - \beta sub 1 = 30$

If a sound has a dB magnitude 30 higher on the decibel scale what is the ratio of their sound energy measurements?

a $A LaTex expression showing \frac{\text{I} sub 2 }{\text{I} sub 1 } = 1,000$

b $A LaTex expression showing \frac{\text{I} sub 2 }{\text{I} sub 1 } = 631$

$A LaTex expression showing \text{dB} = 10\log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \\ \beta sub 2 - \beta sub 1 = 50$

If a sound has a dB magnitude 50 higher on the decibel scale what is the ratio of their sound energy measurements?

a $A LaTex expression showing \frac{\text{I} sub 2 }{\text{I} sub 1 } = 100,000$

b $A LaTex expression showing \frac{\text{I} sub 2 }{\text{I} sub 1 } = 199,526$

$A LaTex expression showing \text{M} = \log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \\ \text{M} sub 2 - \text{M} sub 1 = 1$

If an earthquake has a magnitude 1 higher on the Richter scale what is the ratio of their wave size measurements?

a $A LaTex expression showing \frac{\text{I} sub 2 }{\text{I} sub 1 } = 1$

b $A LaTex expression showing \frac{\text{I} sub 2 }{\text{I} sub 1 } = 10$

$A LaTex expression showing \text{dB} = 10\log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \\ \beta sub 2 - \beta sub 1 = 100$

If a sound has a dB magnitude 100 higher on the decibel scale what is the ratio of their sound energy measurements?

a $A LaTex expression showing \frac{\text{I} sub 2 }{\text{I} sub 1 } = 3.16 multiplied by 10 to the power of 10$

b $A LaTex expression showing \frac{\text{I} sub 2 }{\text{I} sub 1 } = 1 multiplied by 10 to the power of 10$

$A LaTex expression showing \text{dB} = 10\log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \\ \beta sub 2 - \beta sub 1 = 40$

If a sound has a dB magnitude 40 higher on the decibel scale what is the ratio of their sound energy measurements?

a $A LaTex expression showing \frac{\text{I} sub 2 }{\text{I} sub 1 } = 3,162$

b $A LaTex expression showing \frac{\text{I} sub 2 }{\text{I} sub 1 } = 10,000$

$A LaTex expression showing \text{M} = \log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \\ \text{M} sub 2 - \text{M} sub 1 = 7$

If an earthquake has a magnitude 7 higher on the Richter scale what is the ratio of their wave size measurements?

a $A LaTex expression showing \frac{\text{I} sub 2 }{\text{I} sub 1 } = 1 multiplied by 10 to the power of 7$

b $A LaTex expression showing \frac{\text{I} sub 2 }{\text{I} sub 1 } = 3.16 multiplied by 10 to the power of 7$

Logarithmic Scales - Magnitude Difference to Measured Value Ratio