what is the logaritgm of 1/2024 who base is 2
Answers
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Step-by-step explanation:
is any logarithm with base 10. Recall that our number system is base 10; there are ten digits from 0-9, and place value is determined by groups of ten. You can remember a “common logarithm,” then, as any logarithm whose base is our “common” base, 10.
Natural logarithms are different than common logarithms. While the base of a common logarithm is 10, the base of a natural logarithm is the special number e. Although this looks like a variable, it represents a fixed irrational number approximately equal to 2.718281828459. (Like pi, it continues without a repeating pattern in its digits.) e is sometimes called Euler′s number or Napier’s constant, and the letter e was chosen to honor the mathematician Leonhard Euler (pronounced oiler).
e is a complicated but interesting number. Let’s take a closer look at it through the lens of a formula you have seen before: compound interest.
The formula for compound interest is , where A is the amount of money after t years, P is the principal or initial investment, r is the annual interest rate (expressed as a decimal, not a percent), m is the number of compounding periods in a year, and t is the number of years.
Imagine what happens when the compounding happens frequently. If interest is compounded annually, then m = 1. If compounded monthly, then m = 12. Compounding daily would be represented by m = 365; hourly would be represented by m = 8,760. You can see that as the frequency of the compounding periods increases, the value of m increases quickly. Imagine the value of m if interest were compounded each minute or each second!
You can even go more frequently than each second, and eventually get compounding continuously. Look at the values in this table, which looks a lot like the expression multiplied by P in the above formula. As x gets greater, the expression more closely resembles continuous compounding.
x

1
2
10
2.59374…
100
2.70481…
1000
2.71692…
10,000
2.71814…
100,000
2.71826…
1,000,000
2.71828…