I'll be the first to admit that I despised logarithms about as much as my students. Why do we have this strange scale, where not all jumps are equal?
The simple answer is that logs make our life easier, because us human beings have difficulty wrapping our heads around very large or very small numbers. The Richter Scale for earthquakes is a classic example of a logarithmic scale in real life. One of the more interesting facts about this particular logarithmic scale is that it's related to the length of the fault line. The largest earthquake ever recorded was a magnitude 9. By comparison, a theoretical mag 10 earthquake would stretch for tens of thousands of miles ; A practical impossibility but it's fairly easy to grasp that small jumps in numbers here mean huge changes, not small ones.
Decibels, light intensity and and pH as in, my pool water testing kit are all well-known logarithmic scales.
However, " In summation, is the average person really going to ever use a logarithm in real life? Probably not in the "nuts and bolts" sense of the word, but they are useful for many situations. Logarithms work in the same way that a computer chip works in your vehicle--alerting you to that needed oil change, faulty gasket, or open door. Without that chip, we'd be back to the days of troubleshooting a vehicle with a wrench and overalls.
In the same way, there are plenty of real life examples of logarithms working under the hood--you just probably never have a reason to see them.
As logarithms can model so many different phenomena, it's a very handy tool to add to your mathematical toolbox. Show 2 more comments. Active Oldest Votes. Beyond just being an inverse operation, logarithms have a few specific properties that are quite useful in their own right: Logarithms are a convenient way to express large numbers.
I'm sure there are lots of other examples. MathematicalOrchid MathematicalOrchid 5, 4 4 gold badges 27 27 silver badges 42 42 bronze badges. Although we do use logs to solve questions related to exponential decay, it is an exponential function, not a logarithmic function. I don't know anything about your friction example. I suspect there aren't any. Any scientists here to speak on that? Add a comment. Shivam Shah 2 2 bronze badges.
PrimeNumber PrimeNumber Also, that link may die, so you should at least say what is at the link so someone may find it if it changes location.
I am not sure when the edit would me visible. Meantime - scholarworks. It is mostly on the history, less on the uses. Christian Blatter Christian Blatter k 13 13 gold badges silver badges bronze badges.
But what if you're not a chemist? How would you use logs? Ben Millwood Our brains perform a similar trick when we listen to music. But objectively their vibrational frequencies are rising by equal multiplies. We perceive pitch logarithmically. Here is an excellent article which explains the basics of logarithms. Let us look at some of its uses in real life.
If one in X person die as a result of doing some given activity each year, the safety index for that activity is simply the logarithm of X. Higher the safety index, the safer the activity in question. Logarithms helps to shrink the numbers of very high magnitude to a smaller one which our brains can deal with easily. The pH scale measures how acidic or basic a substance is.
It ranges from 0 to A pH of 7 is neutral water. A pH less than 7 is acidic, and a pH greater than 7 is basic. The greater the hydrogen ion concentration, the more acidic the solution. It is defined as. Divide to get t by itself. Use the calculator to evaluate the logarithms.
The money will double in about 7 years. Round to the nearest whole year. According to the U. Census Bureau, the world population in was about 6. That is, it would increase about 1.
If the world population grows by 1. The 1 represents the current population, and the. After two years, the population would be 6. In general, the world population P in billions of people could be estimated for t years after by this formula:.
Part a. P is what you are looking for. Looking at part a first, identify the variables. Use the formula and a calculator to evaluate the exponential expression. According to the problem, the formula finds P in billions of people, so you have Part b. For part b, you want the population to double the 6. Use the formula and the value for P. Divide by 6. Since the variable t is an exponent, take logarithms of both sides. You can use any base, but base 10 or e will allow you to use the calculator easily.
Use the power property of logarithms to get the variable out of the exponent, and then solve for t. The population will hit the doubling point about halfway through the 63 rd year, so you will round up to 64 since the question asks by what year. It will take about 64 years for the population to double, so you have to add 64 to to estimate the year the world population will be Be sure to answer the questions asked.
A particular bacterial colony doubles its population every 15 hours. A scientist running an experiment is starting with bacteria cells. She expects the number of cells to be given by the formula , where t is the number of hours since the experiment started. After how many hours would the scientist expect to have bacteria cells?
Give your answer to the nearest hour.
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