Math 4 - Unit 3 Logarithms TEST

The loudness of a sound is defined in terms of its intensity I by the equation $$dB=10\log\left(\frac{I}{I_0}\right)$$   where I₀ is the minimum intensity audible to the average person (the “threshold of hearing”), $$I_0=1.0\times10^{-12}$$  . How many dB is a baby's cry with $$10^{-1}$$  intensity?

(a)  

The loudness of a sound is defined in terms of its intensity I by the equation $$dB=10\log\left(\frac{I}{I_0}\right)$$   where I₀ is the minimum intensity audible to the average person (the “threshold of hearing”), $$I_0=1.0\times10^{-12}$$  . Sounds become uncomfortable at 120dB. What is the intensity at that level?

The barometric air pressure in inches of mercury at a distance of x miles from the eye of a typical hurricane is modeled by $$P=0.48\ln\left(x+1\right)+27$$  . Match the cities below with their barometric pressure when hurricane Ian was off the coast of Fort Myers, FL. (You may open a new tab for Google Maps)

Write the logarithm expression as a single logarithm

log₅4 + log₅3

$$16=4^{2x-12}$$  

Evaluate the following logarithm:

log₂₇3

Solve the equation.

Round your answer to the nearest thousandth.

$$e^{10v}+6=38$$  

Solve:

$$-6\log_3\left(x-3\right)=-24$$  

Solve:

$$\log_4\left(3x-1\right)=\log_4\left(2x+3\right)$$