log_a (b) [in words - log a of b], is like asking - what power of a equals b. For example: log_10 (100) = 2 because 10^2 = 100 log_2 (16) = 4 because 2^4 = 16
As far as I am aware there is no formula as such to calculate log. The definition of a log is n = B log n , where n is the number being logged and B is the base to which it i…s being logged. This means, log n is the power to which B must be raised to give n. It's not difficult to estimate once you decide what B is. If you choose base 10, which is what we count in usually, the first number in the log is the highest power of 10 which is lower than the number. If the number is 5000 then the 1st number in the log will be 3, as 10 3 = 1000 . log 5000 will be more than 3, less than 4. You can work out approximate values for log n by plotting a graph on ordinary graph paper. If you plot 0 to 10 across and 0 to 1 up the side, then put in the two points properly known (where n=1, log1=0 and for n=10, log10=1). Easily memorable are log of 2, 4, annd 8 which are very close to 0.3, 0.6 and 0.9, but those came straight out of my calculator. ANSWER: There are several ways to calculate logarithms. Euler could calculate logarithms using a binary search and the geometric mean. There is another way to calculate the log using the natural logarithm, base e. I developed my own method using squares, and there is a link provided. (MORE)
Pretty much, yeah. It's just another way of expressing exponents. Say you know the following: (we'll start off easily) 16 = 4 2 You could also write that as: log …4 16 = 2 Algebraically, a = b c so, log b a = c (b is known as the base, so it is read: log base b of a equals c) Also, log b a = (log a) / (log b) (MORE)
The main use for a logarithm is to find an exponent. If N = a^x Then if we are told to find that exponent of the base (b) that will equal that value of N then the notati…on is: log N ....b And the result is x = log N ..........b Such that b^x = N N is often just called the "Number", but it is the actuall value of the indicated power. b is the base (of the indicated power), and x is the exponent (of the indicated power). We see that the main use of a logarithm function is to find an exponent. The main use for the antilog function is to find the value of N given the base (b) and the exponent (x) (MORE)
Logarithms are kind of like reverse exponents. log is just a quick way to write log 10. log e can also be shortened to ln. Logarithm form, lob b N=L, can also be written as …b L =N. For example, log 3 9=2 because 3 2 =9. (MORE)
The power operation, for example: x = 2 10 (answer: x = 1024) has two inverse operations, depending which of the two numbers you have to solve for. To solve for the b…ase if you know the exponent is called calculating the root. For example: x 10 = 1024 This is asking for the tenth root of 1024. The other inverse is if the exponent is unknown, for example: 2 x = 1024 Solving this problem is called calculating the logarithm. (MORE)
A logarithm is the inverse of exponentiation; that is, the log of anumber is the exponent to which its base is raised to produce thatnumber. For example common logarithms have… base 10; the value N ofthe log of a number x is found as 10 to the N exponent equals x.For example the log 20 = N; 10 to the N exponent = 20; N = 1.301 (MORE)