A set of college algebra problems on logarithmic and exponential function with answers, are presented. The solutions are at the bottom of the page.

Let the logarithmic
function f be defined by f(x) = 2ln(2x  1).
a) Find the domain of f.
b) Find vertical asymptote of the graph of f.

Let the exponential function h be defined by h(x) = 2 + e^{x}
a) Find the range of h.
b) Find the horizontal asymptote of the graph of h.

The population of city A changes according to the exponential function
A(t) = 2.9 (2) ^{ 0.11 t} (millions)
and the population of city B changes according to the exponential function
B(t) = 1.7 (2) ^{ 0.17 t} (millions)
where t = 0 correspond to 2009.
a) Which city had larger population in 2009?
b) When will the sizes of the populations of the two cities be equal?

Find the inverse of the logarithmic function f defined by f(x) = 2 Log_{5} (2x  8) + 3

Find the inverse of the exponential function h defined by h(x) =  2*3^{3x + 9}  4

Solve the logarithmic equation defined by
ln(2x  2) + ln(4x  3) = 2 ln(2x)

A, B and k in the exponential function f given by
f(x) = A e^{k x} + B
are constants. Find A, B and k if f(0) = 1 and f(1) = 2 and the graph of f has a horizontal asymptote y = 4.

