Pardon the interruption.
Now, back to our regular programming. Some properties of logarithms include:
There is no limit to the number of digits that can have in a logarithm (e.g., 2^5 gives us the answer 25) The base does not matter for a logarithm For example, 5 logged 10 and 5 logged 100000 both yield 125 In order for a result to make sense, this means that at least one of the original numbers must be between 1 and 9.
Logarithms convert large numbers to small, manageable ones. For example, take the number 10^9 and use a logarithmic calculators to calculate its log base 10 value of 3. What that means is that you can now multiply all those 9’s by 3 … a little easier, but not really much!
Logarithms have many uses, but they are primarily used to correct for exponential growths and decay.
A logarithm with base ? of ? is the power to which you must raise ? so that its value is equal to ?. For example, if we use log 10 as the base (so that a number can be encoded using powers of 10), then 100 = 10^3= 1000. If we use log 2 as the base (where a number can be encoded by binary digits) then 2^4=16 also considered very large with about 67 more digits than would fit in any book or spreadsheet on Earth.
Logarithms, or logs, are inverse functions in mathematics. In other words, think of a number line where every number from 0 to 10 (and infinite numbers on either end) represents a “point” on the number line. On this hypothetical picture of such an imaginary mathematical graph/line, if we were to take all the points from 1 and 2 and 3 and 4… up until we had moved through all the numbers up to 10 that represent “points” on our age line, then they would be consecutive representations along the same horizontal graph line. Logs are what happen when we think about those particular locations above as single symbols for each point in time with regard to that numerical order they now have for us.
- Logarithms are approximately related to percentages.
- Logarithms are a way of reducing something very large from one number to another much smaller one.
- When you add two positive numbers, the logarithm is equal to the first number minus the second number multiplied by their product raised to that power.
- Simplistic properties of logarithms include that anything you can do with multiplication, division or addition can be replicated by doing it on the logs of two related numbers.
It can be misleading to “just look it up”, because logarithms are inherently complicated and often have multiple properties.
For example,
log(a2) = 2 log(a),
x^y is a natural base-y logarithm function. A property of one which we will explore in this answer is its inverse or exponential function – y = e^x. This property implies that at any point below 1, the closer you get to 0 (e^(-x)), the bigger the number becomes!
1.log_x(y) is the same as log_y(x) (i.e. 10^5=1000.)
2.log_b((a/b)) is the same as log_(a)/log_(b) (i.e. log 125000 = log 1/10000), and so on…
3.(In most hard-limiting cases, biological meaning of ‘rate’).A less restrictive rate law might be written as L = k*exp(-t/T). A limiting case of that could be written, for example, as L=k*ln(2*T/(T1+t)).
The logarithm of a product is the sum of the logarithms.
The logarithm of a quotient is the difference in logs.
Logarithms help you multiply or divide two numbers, even if they are so large that most calculators can’t hold them. If you’re multiplying and your answer has a high number in the exponent, it would take too long to do all of the multiplications. In this case, it’s really simple to find the logarithm of the base 10 of your numbers to get the result because logs allow you to convert a problem into an easier problem. The same logic applies when dividing two numbers with one or more digits in their exponents 2-8 (this is called base 10).
– Logarithms are the inverses of exponential functions.
– The logarithm is also called a common logarithm because it is used in many everyday situations, such as calculating mortgage interest and biological growth rates.
– Logarithms come up in mathematics, physics, chemistry, astronomy, engineering and other branches of science related to these subjects because they divide difficult computations by easy calculations
