0
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
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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
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.
How many lines of symmetry does the number 0?
There are an infinite amount.
Is there a subset to 0?
There is, because {0} has one element, 0. The set {0} therefore can have infinite sets, providing that, all sets are either null or has one element, 0.
