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What is the value of loge if base is not equal to e?
You can calculate log to any base by using: logb(x) = ln(x) / ln(b) [ln is natural log], so if you have logb(e) = ln(e) / ln(b) = 1 / ln(b)
What is the value of log 500?
The value of log 500 depends on the base of the logarithm. If the base is 10 (common logarithm), then log 500 is approximately 2.69897. If the base is e (natural logarithm), then log_e 500 is approximately 6.2146. The logarithm function is the inverse of exponentiation, so log 500 represents the power to which the base must be raised to equal 500.
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.
How do you write expressions in exponential form of the numbers 3 and 5?
Using the natural (base e) logs, written as "ln", 3 is eln(3) and 5 is eln(5). Or in base 10, 3=10log(3) and 5=10log(5). Check it out by taking log of both sides: log(3) = log(10log(3)) = log(3) x log(10) =log(3) x 1=log(3).
What is the derivative of log x-2?
The formula for finding the derivative of a log function of any "a" base is (dy/dx)log base a (x) = 1/((x)ln(a)) If we're talking about base "e" (natural logs) the answer is 1/(x-2) I think you're asking for the derivative of y = logx2. It's (-logx2)/(x(lnx)).
What is log 100 base e?
log(e)100 = log(10)100 / log(10)e = log(10)100 / log(10) 2.71828.... = 2/ 0.43429448... = 4.605170186..... (The answer). NB Note the change of log base to '10' However, on a calculator type in ;- 'ln' (NOT log). '100' '=' The answer shown os 4.605....
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).
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 evaluate log1.02(3)?
You calculate log(3) / log(1.02) - using the same base for both. For example, both to the base "e", or both to the base "10" (those are the two options available on most calculators).
What number has a log of 8.0573-10?
18.057299999999998
What is log 50 to the base 0.1?
log0.1 50 = log10 50 / log10 0.1 ~= -1.699 To work out the log to any base b, logs to another base can be used: When logs are taken of a number to a power, then the power is multiplied by the log of the number, that is: log(bn) = n log b Taking logs to base b the power of b that equals the original number is being found, that is if: bn = m then logb m = n So, by using the logs to a base to which the answer can be known, the log to any base can be calculated: bn = m => n log b = log m => n = log m / log b => logb m = log m / log b as long as the same base is used for the logs on the right. It is normal to use base 10 or base e which are found on calculator buttons marked log (base 10) and ln (log natural - base e).
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.
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 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).
Differentiate log x?
The derivative of ln x, the natural logarithm, is 1/x.Otherwise, given the identity logbx = log(x)/log(b), we know that the derivative of logbx = 1/(x*log b).ProofThe derivative of ln x follows quickly once we know that the derivative of ex is itself. Let y = ln x (we're interested in knowing dy/dx)Then ey = xDifferentiate both sides to get ey dy/dx = 1Substitute ey = x to get x dy/dx = 1, or dy/dx = 1/x.Differentiation of log (base 10) xlog (base 10) x= log (base e) x * log (base 10) ed/dx [ log (base 10) x ]= d/dx [ log (base e) x * log (base 10) e ]= [log(base 10) e] / x= 1 / x ln(10)
What is the difference between log and ln?
Log is a logarithm with any arbitrary base, for example log_10 100=2. Ln is a logarithm with a base of e(Euler's number), which is 2.71828 18284 59045 23536...
How do you convert natural log into binary log?
Use the equation. ln 'x' = log(2) x / log(2) n. '2' being the binary system of 10101010.... However, it may be easier to understand using base '10'. lnx' = log(10)x / log(10)'e' NB This will give a different answer to log base '2' (binary). NNB Within logarithms you can change the base value tp any other base using the above equation. Calculators give logs to base '10'(log) and base 'e' (2.71828.....)(ln). However, you can use any number as a base value e.g. '100' say , or '79' say. providing you use the above eq'n.
