Create a free Team What is Teams? Learn more. What is the point of logarithms? How are they used? Asked 10 years, 10 months ago. Active 2 years, 5 months ago. Viewed 99k times. NickDelin NickDelin. For instance, pH is a more "manageable" number than the corresponding concentration of hydronium ions in an acid. There is a list at the Wikipedia article: en. Can you ask a more precise question? What do you mean by " the point "? What do you already know about logarithms?
What else do you want to know or do not understand? 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 41 41 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 From the left, it grows rapidly, but that growth is dampened as time passes to where it reaches a maximum. Below is the graph of a logistic function. Compound interest is accrued when interest is earned not only on principal, but on previously accrued interest: it is interest on interest. Fundamentally, compound interest is an application of exponential functions that is found very commonly in every day life. Interest is, generally, a fee charged for the borrowing of money.
The two classic cases are 1 interest accrued as part of loan and 2 interest accrued in a savings or other account. In the first case the client owes the amount borrowed plus the interest. In the second, the bank pays the client interest for maintaining money in the account.
If you are the client, you are losing money in the first case and earning money in the second. The client does not, for example, add or withdraw funds from the savings account after the initial deposit the principal is made. In simple interest, interest is accrued on the principal alone. This means that the amount of interest earned in each compounding period is the same because interest is earned based on the principal which remains unchanged.
In compound interest, interest is accrued on both the principal and on prior interest earned. For this reason, if all other conditions are the same principal, rate, time elapsed and frequency of interest payments compound interest grows at a faster rate than simple interest. The amount of interest earned increases with each compounding period. Let us begin by determining the interest at the end of the first year.
The interest earned at the end of the year is:. The table below shows the calculations, interest earned and total amount in the account after 1, 2, 3, 4, and n years. Calculations of interest earned and amount in the account for Example 1. Compound interest is not linear, but exponential in form.
That is, the amount of interest earned is not constant but instead changes with time based on the total amount of the amount in the account. The equation representing investment value as a function of principal, interest rate, period and time is:. The amount in the account after one year is:. This is the exact amount that was in the account after the first year using simple interest.
That is because the difference is that compound interest earns interest on both the principal and prior interest. At the end of the first year there was no prior interest in the account. We will see differences between simple and compound interest in this, and similar problems, in the second year. We obtain:. This might not seem like a lot but the amount of interest earned will continue to increase each year as there is more and more money in the account.
Every year the interest earned will be higher than in the previous year, whereas in simple interest the amount each year is fixed. The amount in the account is greater each year beginning with year two when using compound interest rather than simple interest.
However, because the principal is so small and the number of years elapsed only 4, it does not appear that the difference between the two example is that great. Let us consider one last problem where we let the time elapsed be much greater. The biggest differences between the amount of money in an account using simple versus compound interest are seen over extended periods of time. To highlight this, we return the the examples we did prior and now consider how much money is in each account after 50 years.
The more frequent the compounding periods the more interest is accrued. Therefore, if one deposits money into a bank account that earns compound interest, and does not add or withdraw any additional funds, the amount of money in the bank would increase as the number of compounding periods per year increases.
You earn the most interest when interest is compounded continuously. The graph shows that the more frequent the number of compounding periods the more interest is accrued and shows this visually for yearly, quarterly, monthly and continuous compounding.
Given that the more frequent the compounding periods per year, the more interest is accrued it might come as a surprise that money deposited into a bank account accrues compound interest continuously. You might expect the bank would choose a smaller number of compounding periods in order to pay out less in interest, but this is not the case. You do not add or withdraw money from the account. This is a simplification of the prior formula used because of the specific conditions of this most recent situation.
In the earthquake, a Seismic wave produces which travels through the Earth layer. The seismic wave gives out an energy that causes the earth to shake and also gives out low frequency acoustic energy. Read More : Maths Short Tricks Now, these seismic waves is recorded by the seismograph instrument and its output is the seismographs graph. This occurs directly beneath the epicenter, at a distance known as the focal depth.
The amplitude of the seismic waves decreases with distance. Now, the instrument seismograph is based on a logarithmic scale, which is developed by Charles Richter in devised the first magnitude scale for measuring earthquake magnitude. This is commonly known as the Richter scale. T he magnitude of an earthquake is calculated by comparing the maximum amplitude of the signal with this reference event at a specific distance.
The Richter scale is a base logarithmic scale, which defines magnitude as the logarithm of the ratio of the amplitude of the seismic waves to an arbitrary, minor amplitude. The magnitude of the standard earthquake is. Since the Richter scale is a base logarithmic scale, each number increase on the Richter scale indicates an intensity ten times stronger than the previous number on the scale.
Read: Why Log is not defined for the negative base. For example: if we note the magnitude of the earthquake on the Richter scale as 2, then the other next magnitude on the scale is explained in the following table.
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