Common and Natural Logarithmic Functions 2?

Question

Find the domain of the given functions (that is, the largest set of real numbers for which the rule produces well-defined real numbers)

43. h(x)= log (-x)

Please show all work and formulas used to find the answer.

I Thank You All In Advance

Answer 1

The "common log" function, i.e., log-base10, is defined, as all log functions only on (0, +infinity). Thus, your composite function,

f(x) = g(h(x)) for g(x) = logx, and h(x) = -x

is defined only for values of h(x) on the range (0, +infinity). That is,, the range of h is the domain of g. Hence, -x (range of h) in (0, +infinity) implies x in (-infinity, 0).

Answer 2

while no longer something is writen by ability of the backside of the log then the backside is 10: log .001 = -3 <--- so this log is base 10 use the log rule: log(base x) a =b is like x^b=a so on your case: log (base 10) .001= -3 is like 10^-3= .001 that's like: 10^-3 = 10^-3 that's actual by way of fact while the potential is adverse the form will become a fragment and so 10^-3 = a million/one hundred = .001 ithe comparable approach is actual for the different question as nicely log(base 10 )3= .4771 by way of fact 10^.4771 = 3 i desire this helped you :+)

Answer 3

since the domain of log(x) is all real numbers x>0
log(-x) should be all real numbers x < 0

Answer 4

0 > x > - (infinite)

- (infinite) > h > + (infinite)