2016年3月21日 · The exponential function is one-one on its domain, so its inverse - the Real natural logarithm, ln x - is well defined, with domain (0, oo) and range RR. The Complex logarithm is somewhat messier. z -> e^z is many to one since e^(2pii) = 1. So we need to restrict the domain of e^z or the range of ln z in order to be able to define ln z as a ...

2018年6月24日 · D:x in (0,oo) The logarithm (I'm using natural log here, but it works for any base) is defined as: logx=a iff x=e^a This means the domain of logx is the set of all values that e^a can be. Since e is positive and a positive number raised to any power is still positive, we know that e^a is always positive. Therefore, the domain of logx is all positive real numbers, or written symbolically it is ...

2017年12月25日 · For domain, the argument of the logarithm must be greater than 0. Domain: \{x | x > 6, x \in \mathbb{R}} Range: \{y | y \in \mathbb{R}} For domain: The argument of the logarithm (stuff inside the log) must be greater than 0. This is because logarithm can be viewed as the inverse of an exponential function.

For example, to approximate #ln(7)#, split the interval #[1, 7]# into a number of strips of equal width, and sum the areas of the trapezoids with vertices:

2018年1月6日 · The domain of a function includes all possible x values of a function, and the range includes all possible y values of a function. Domain: (2,oo){x|x>2} since log is undefined for 0 or negative values Range: (-oo,oo){y|yinRR} This can be verified with a graph: graph{log(x-2)}

2015年7月19日 · f(x) = log_5 x is the inverse of the function e(x) = 5^x which has domain (-oo, oo) and range (0, oo). So the domain of log_5 x is (0, oo) and range is (-oo, oo) The domain of e(x) = 5^x is the whole of RR, that is (-oo,oo), but its range is (0, oo). So the domain of its inverse y = log_5 x is (0,oo) and its range is (-oo,oo)

2017年12月13日 · Range: y in RR Domain: x in RR To answer this question we must consider our log laws: alphalogbeta = logbeta^alpha So using the knowledge: y = log2^x => y = xlog2 Now this is just linear! We know log2 approx 0.301 => y = 0.301x Now we see by a sketch: graph{y = 0.301x [-10, 10, -5, 5]} That all x and all y are defined, yielding: x in RR and y in RR

2016年10月5日 · The domain is: D=(2;+oo). See explanation. The domain of a function is the biggest subset of real numbers set for which the value of function is defined. Here we have to assume that x-2>0 because logarythm is only defined for positive numbers. So we get: x-2>0 x>2 If we write this set as an interval we get: x in (2;+oo)

2017年5月11日 · Domain: x> 9 or (9,oo) The range of y is all of RR or (oo, oo) y= log(x-9) . Domain: x-9>0 or x> 9 or (9,oo) Range : As x approaches closer and closer to 9 from right, y gets more and more negative. So Range is all real numbers i.e (oo, oo) graph{log(x-9) [-40, 40, …

2018年3月3日 · x>1 (domain), yinRR (range) The domain of a function is the set of all possible x values that it is defined for, and the range is the set of all possible y values. To make this more concrete, I'll rewrite this as: y=ln(x-1) Domain: The function lnx is defined only for all positive numbers. This means the value we're taking the natural log (ln) of (x-1) has to be greater than 0. Our inequality ...