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# Logarithmic Word Problems

## Natural Logarithm Word Problem example

If a beam of light that has intensity I is projected vertically downward into water, then its intensity I(x) at a depth of x meters is

At what depth is the intensity  its value at the surface?

Solution to this Logarithms practice problem is given in the video below!

## Common Logarithm Word Problem example question

The Beer-Lambert law states that the amount of light I that penetrates to a depth of x meters in an ocean is given by

a) Solve for x in terms of common logarithms

b) If c = , approximate the depth when  . This determines the photic zone where photosynthesis can take place.

Solution to this Logarithms practice problem is given in the video below!

## Common Logarithm Word Problem example problem

A drug is eliminated from the body through urine. Suppose that for a dose of 10 milligrams, the amount A(t) remaining in the body t hours later is given by

and that the drug to be effective, at least 2 milligrams must be in the body.

a) Determine the time when 2 milligrams are left in the body

b) What is the half-life of the drug?

Solution to this Logarithms practice problem is given in the video below!

## Newton’s Law of Cooling example

Police arrive at a murder scene at 1:00 AM and immediately record the body’s temperature which was 92 degrees °F. At 3:00 AM, after thoroughly inspecting and fingerprinting the area, they again took the temperature of the body which had dropped to 87 degrees °F. The temperature of the crime scene has remained at a constant 71 degrees °F. Determine the time when the person was murdered. (Assume that the victim was healthy at the time of death. That is, assume that the temperature of the body at the time of death was 98.6 degrees °F).

Solution to this Law of Cooling Logarithms practice problem is given in the video below!