Question

Which of the following is true?

1) the base of a logarithmic function can be zero
2) a logarithmic function is the inverse of a rational function
3) the domain of the function f(x)= (log5)x is all real numbers less than zero
4) the range of the function f(x)= (log5)x includes rational numbers

Answer 1

1) is false
2) is false, log is inverse of exponential function
3) is false, domain of log is x>0
4) is true, range of log is all real numbers which includes rational

Answer 2

\[y=\log_a(x)=\frac{lnx}{lna}\]
x>0
a can be in the set (0,1) U (1,inf)

Answer 3

good explanation for that 1

Answer 4

logarithmic function is inverse of exponential function

Answer 5

\[y=\log_5(x)=\frac{lnx}{\ln5}\]
x>0

Answer 6

4) example
\[y=\log_5(5)=1\]
1 is rational