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The log is the answer to the question, "To what power must I raise a number (the base) to obtain a certain other number?" In this case (assuming a base 10), you are looking for the solution to the equation 10x = 1. The answer, of course, is x = 0.
The reason it is "of course" is because 10x divided by 10x ie 1, is found by subtracting the powers (which are logarithms) to give 100
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Why log 0 is infinite?
the definition of log N = X is 10 to the X power =N for log 0 we have 10 to the x power = 0 The solution for x is that x is very large (infinite) and negative, that is, minus infinity As N gets smaller and smaller, log N approaches minus infinity log 1 = 0 log .1 = -1 log .001 = -3 log .000001 = -6 log 0 = -infinity
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
What is the value of log 1?
log 1 = 0 if log of base 10 of a number, N, is X logN = X means 10 to the X power = N 10^x = 1 x = 0 since 10^0 = 1
What is x squared 8?
We know that a logarithm is an exponent. Let x^8 = a. For x > 0, x is different than 1, and a > 0, x^8 = a is equal to the log with base x of a = 8
How do you show log x is convex?
Log x is defined only for x > 0. The first derivative of log x is 1/x, which, for x > 0 is also > 0 The second derivative of log x = -1/x2 is always negative over the valid domain for x. Together, these derivatives show that log x is a strictly monotonic increasing function of x and that its rate of increase is always decreasing. Consequently log x is convex.
