For the given functions,

f(x) = log_ex
g(x) = - ln(5x)

(i) Graph in the same cartesian plane
(ii) Identify all asymptotes
(iii) Identify Domain and Range

a) (i) Graph: Graph of f(x) and g(x) with asymptotes at x=0, showing points (0.2,0) and (1,0).

(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: Graph of g(x) and f(x) with asymptotes at x=0, showing points (0.2,0) and (1,0).

(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: Graph of f(x) and g(x) with asymptotes at x=0, showing points (1,0) and (2,0).

(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: Graph of g(x) and f(x) with asymptotes at x=0, showing points (1,0) and (2,0).

(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

Solve the following logarithmic equation: