6. Exponential & Logarithmic Functions
Introduction to Logarithms
50PRACTICE PROBLEM
For the given functions,
f(x) = logex
g(x) = - ln(5x)
(i) Graph in the same cartesian plane
(ii) Identify all asymptotes
(iii) Identify Domain and Range
a) (i) Graph: ![](https://lightcat-files.s3.amazonaws.com/problem_images/2fbe99f005607b9d-1673529668219.jpg)
(ii) Asymptotes f(x): x = 0, g(x): x = 0,
(iii) Domain f(x): x > 0; g(x): x > 0; Range f(x): all real values; g(x): all real values
b) (i) Graph: ![](https://lightcat-files.s3.amazonaws.com/problem_images/ad5d72903708d89e-1673529709750.jpg)
(ii) Asymptotes f(x): x = 0, g(x): x = 0,
(iii) Domain f(x): x < 0; g(x): x < 0; Range f(x): f(x) > 0; g(x): g(x) > 0
c) (i) Graph: ![](https://lightcat-files.s3.amazonaws.com/problem_images/02d3915ff7e3fba9-1673529778849.jpg)
(ii) Asymptotes f(x): x = 0, g(x): x = 1,
(iii) Domain f(x): x > 0; g(x): x > 1; Range f(x): all real values; g(x): all real values
d) (i) Graph: ![](https://lightcat-files.s3.amazonaws.com/problem_images/d033c019b10468ca-1673529820096.jpg)
(ii) Asymptotes f(x): x = 1, g(x): x = 0,
(iii) Domain f(x): x > 1; g(x): x > 0; Range f(x): all real values; g(x): all real values
For the given functions,
f(x) = logex
g(x) = - ln(5x)
(i) Graph in the same cartesian plane
(ii) Identify all asymptotes
(iii) Identify Domain and Range
a) (i) Graph:
(ii) Asymptotes f(x): x = 0, g(x): x = 0,
(iii) Domain f(x): x > 0; g(x): x > 0; Range f(x): all real values; g(x): all real values
b) (i) Graph:
(ii) Asymptotes f(x): x = 0, g(x): x = 0,
(iii) Domain f(x): x < 0; g(x): x < 0; Range f(x): f(x) > 0; g(x): g(x) > 0
c) (i) Graph:
(ii) Asymptotes f(x): x = 0, g(x): x = 1,
(iii) Domain f(x): x > 0; g(x): x > 1; Range f(x): all real values; g(x): all real values
d) (i) Graph:
(ii) Asymptotes f(x): x = 1, g(x): x = 0,
(iii) Domain f(x): x > 1; g(x): x > 0; Range f(x): all real values; g(x): all real values