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Why natural log has base e?
Because when the system of logarithms with the base 'e' was defined and tabulated, it was entitled with the identifying label of "Natural Logarithms". ---------------------------------- My improvement: The natural log base is e (a numerical constant of about 2.718). It is chosen as a log base since there is a mathematical series (a "string" of mathematical numerical terms to be summed) for calculating a logarithm (ie. exponent of the base) of a number, which has a base of e. Series for calculating logarithms with bases other than e have basically not been developed.
What is the natural log of x?
It means the logarithm to the base e. The number "e" is approximately 2.71828... In other words, if you ask, for instance, "what's the natural logarithm of 100", that's equivalent to asking "to what number must I raise 'e', to get the answer 100". The solution of the equation e^x = 100 in this example.
How do you convert natural log into binary log?
log2x = log x / log 2 On the right side, you can use logarithm in any base (calculators usually provide base-10 and base-e), just be sure to use the same base in both cases. Thus: log2x = ln x / ln 2 or: log2x = log10x / log102
What is log base 3 of (x plus 1) log base 2 of (x-1)?
The browser which is used for posting questions is almost totally useless for mathematical questions since it blocks most symbols.I am assuming that your question is about log base 3 of (x plus 1) plus log base 2 of (x-1).{log[(x + 1)^log2} + {log[(x - 1)^log3}/log(3^log2) where all the logs are to the same base - whichever you want. The denominator can also be written as log(3^log2)This can be simplified (?) to log{[(x + 1)^log2*(x - 1)^log3}/log(3^log2).As mentioned above, the expression can be to any base and so the expression becomesin base 2: log{[(x + 1)*(x - 1)^log3}/log(3) andin base 3: log{[(x + 1)^log2*(x - 1)}/log(2)
How do you compare logarithms with different bases?
You can convert to the same base, by the identity: logab = log b / log a (where the latter two logs are in any base, but both in the same base).
What is full form of LOG?
"Log" is short for Logarithm and can be to any base.The Logarithm of a number is the number to which the base has to be raised to get that number; that is why there are no logarithms for negative numbers. For example: 10² = 100 → log to base 10 of 100 is 2.There are two specific abbreviations:lg is the log to base 10ln is the log to base e - e is Euler's number and is approximately 2.71828184; logs to base e are known as natural logs.On an electronic calculator the [log] button takes logarithms to base 10. The inverse function (anti-log) is marked as 10^x.Similarly the [ln] button takes logs to base e, with the inverse function marked as e^x.
What is the same thing as log base e?
log base e = ln.
Solve ln y equals xln e?
ln is the natural logarithm. That is it is defined as log base e. As we all know from school, log base 10 of 10 = 1 just as log base 3 of 3 = 1, so, likewise, log base e of e = 1 and 1.x = x. so we have ln y = x. Relace ln with log base e, and you should get y = ex
How do I solve the equation e to the power of x equals 2 using logarithms?
When the logarithm is taken of any number to a power the result is that power times the log of the number; so taking logs of both sides gives: e^x = 2 → log(e^x) = log 2 → x log e = log 2 Dividing both sides by log e gives: x = (log 2)/(log e) The value of the logarithm of the base when taken to that base is 1. The logarithms can be taken to any base you like, however, if the base is e (natural logs, written as ln), then ln e = 1 which gives x = (ln 2)/1 = ln 2 This is in fact the definition of a logarithm: the logarithm to a specific base of a number is the power of the base which equals that number. In this case ln 2 is the number x such that e^x = 2. ---------------------------------------------------- This also means that you can calculate logs to any base if you can find logs to a specific base: log (b^x) = y → x log b = log y → x = (log y)/(log b) In other words, the log of a number to a given base, is the log of that number using any [second] base you like divided by the log of the base to the same [second] base. eg log₂ 8 = ln 8 / ln 2 = 2.7094... / 0.6931... = 3 since log₂ 8 = 3 it means 2³ = 8 (which is true).
What number has a log of 8.0573-10?
18.057299999999998
What is a log in Math?
a log is the 'undo-er' of powers, kind of like division is the 'undo-er' of multiplication. EX: 102 = 100, then log10(100) = 2 103 = 1000, then log10(1000) = 3, in this example, we are using log base 10, this is a default base and sometimes isn't even wirten. e is probably the most common base but log base e is more simply called the natural log, or ln. so in general: logx(m) = N means that xN = m so log5(125) = 3 because 53 = 125.
Problem find the values of log 100 to the base 0.1?
log 8.008
How do you solve log x plus log 8 equals 1?
log(x)+log(8)=1 log(8x)=1 8x=e x=e/8 You're welcome. e is the irrational number 2.7....... Often log refers to base 10 and ln refers to base e, so the answer could be x=10/8
What is the logarithm of 100?
logarithm of 100 = 2. If there is not a subscript number on your log, you assume it to be 10. In other words, the little subscript would be the base if you were raising it to a power, and the big number is the answer of the power. For example, log (base 10) 100 = 2 because 10 (the base) raised to a power of 2 (the log answer) = 100 (the number you just took the log of.)
What 100 is to 2 in base 10?
natural log
What is the natural log of 100?
The natural log of 100 is about 4.605. The transcendental number e (about 2.718281828) raised to the power of 4.605 is 100.
What is Log S?
In mathematics, the logarithm function is denoted by "log". The base of the logarithm is typically specified, for example, "Log S" usually refers to the logarithm of S to a certain base (e.g., base 10 or base e).
