Rewrite the following logarithmic function using the properties of logarithms. Then, use the written function to graph it:

f(x) = log₆ [(x + 2)/36]

Find the domain of the following function: f(x) = log[(x - 3)/(x + 7)]

Express the following equation in exponential form and solve the equation for x: log₂ x = -4

Evaluate the following expression: log₁₁ √11

Which of the following is the exponential form of 6 = log₂ x?

For the given functions,

f(x) = log x
g(x) = - log(x - 1)

(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

Transform the following equation to its exponential form.

log₂2048 = y