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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 = x
Differentiate both sides to get ey dy/dx = 1
Substitute ey = x to get x dy/dx = 1, or dy/dx = 1/x.
Differentiation of log (base 10) x
log (base 10) x
= log (base e) x * log (base 10) e
d/dx [ log (base 10) x ]
= d/dx [ log (base e) x * log (base 10) e ]
= [log(base 10) e] / x
= 1 / x ln(10)
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What is log to the third power equal to?
Log (x^3) = 3 log(x) Log of x to the third power is three times log of x.
Rules of log?
Here are a few, note x>0 and y>0 and a&b not = 1 * log (xy) = log(x) + log(y) * log(x/y) = log(x) - log(y) * loga(x) = logb(x)*loga(b) * logb(bn) = n * log(xa) = a*log(x) * logb(b) = 1 * logb(1) = 0
Log9x plus log x equals 4log10?
log(9x) + log(x) = 4log(10)log(9) + log(x) + log(x) = 4log(10)2log(x) = 4log(10) - log(9)log(x2) = log(104) - log(9)log(x2) = log(104/9)x2 = 104/9x = 102/3x = 33 and 1/3
Log base 2 of x - log base 2 of x-23?
log base 2 of [x/(x - 23)]
If 3 log x - 2 log y?
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