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Most people do not mean the same thing when they write "ln" and "log". Both refer to a logarithm, but the base for "ln" is the number e (a special number roughly equal to 2.1781) while the base for "log" is 10, unless otherwise specified. "ln" is called the natural logarithm and "log" is called the common logarithm when it refers to the base 10 logarithm.
A quick example of how they are different:
log 10,000 = 4
ln 10,000 = 9.21
The reason for this is that the logarithm is the inverse of (that is, it undoes) exponentiation. The first example asks "what power do I have to raise 10 to in order to get 10,000?" The exponentiation related to the first example is 104 = 10,000. The second example asks "what power do I have to raise e to in order to get 10,000?" The exponentiation related to it is e9.21 = 10,000.
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What measurement is LN?
Natural log.
How do you find exponent N in 126 n12?
126 = n^12 12 = log(base n)126 Since log(base n)(126) = log 126/log n or log(base n)(126) = ln 126/ln n we write: 12 = ln 126/ln n 12 ln n = ln 126 ln n = ln 126/12 ln n = 0.4030234922 rewrite the natural logarithm showing base e (optional) log(base e)(n)= 0.4030234922 e^0.4030234922 = n Check e^0.4030234922 126 = (e^0.4030234922)^12 ? 126 = e^4.836281907 ? 126 = 126 True
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 exponential equation is equivalent to the logarithmic equation e exponent a equals 47.38?
The given equation is exponential, not logarithmic!The logarithmic equation equivalent to ea= 47.38 isa = ln(47.38)ora = log(47.38)/log(e)The given equation is exponential, not logarithmic!The logarithmic equation equivalent to ea= 47.38 isa = ln(47.38)ora = log(47.38)/log(e)The given equation is exponential, not logarithmic!The logarithmic equation equivalent to ea= 47.38 isa = ln(47.38)ora = log(47.38)/log(e)The given equation is exponential, not logarithmic!The logarithmic equation equivalent to ea= 47.38 isa = ln(47.38)ora = log(47.38)/log(e)
Graph Inverse function of the exponential function?
An exponential function is of the form y = a^x, where a is a constant. The inverse of this is x = a^y --> y = ln(x)/ln(a), where ln() means the natural log.
