The log(infinity) does not exist. It is impossible to evaluate because infinity is not a number. When evaluating limits infinity is a special case of a nonexistent limit. The limit of the log(x) as x approaches infinity is infinity because log(x) increases without bound when x gets extremely large.
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For log (x), as the number x increases infinitely, log (x) also increases infinitely, though at a slower rate.
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There is no number greater than infinity. Infinity is defined to be greater than any number, so there can not be two numbers, both infinity, that are different.However, when dealing with limits, one can approach a non-infinite value for a function involving infinity. Take, for example, 2x divided by x, when x is infinity. That value is indeterminate, because infinity divided by infinity is defined as indeterminate, and 2 times infinity is still infinity.But, if you look at the limit of 2x divided by x, as x approaches infinity, you do get a value, and that value is 2. This does not mean that 2x when x is infinity is twice infinity, it just means that, right before x becomes infinity, the ratio is right before 2.Infinity should not be thought of as a number, but rather as a direction. Whereas a number represents a specific quantity, infinity does not define given quantity. (If you started counting really fast for billions of years, you would never get to infinity.) There are, however, different "sizes of infinity." Aleph-null, for example, is the infinity that describes the size of the natural numbers (0,1,2,3,4....) The infinity that describes the size of the real numbers is much larger than aleph-null, for between any two natural numbers, there are infinite real numbers.Anyway, to improve upon the answer above, it is not meaningful to say "when x is infinity," because, as explained above, no number can "be" infinity. A number can approach infinity, that is to say, get larger and larger and larger, but it will never get there. Because infinity is not a number, there is no point in asking what number is more than infinity.
log 1.630 = 0.2122 I just put 1.63 into a calculator, pressed Log, and read the answer to four significant places.
Because the argument of the sine function can have any real value. In fact, it can extend beyond that but that is for more advanced level students.
The graph of y = log(x) is defined only for x>0. The graph is a monotonic increasing function over its domain. It starts from an asymptotic "minus infinity" when x approaches 0. It passes through the value y = 0 when x = 1. The graph is illustrated at the link below.