Find x for the following equation.

ln(4x + 3) + ln(x - 1) - 2lnx = 0

Solve the following logarithmic equation and, if needed, use a calculator to approximate your solution to two decimal places.

8 ln(11x) = 32

Find x. g(x - 3) = d(4x + 8)

Consider the one-to-one function f(x) = 19^x - 3. Determine the equation of its inverse function.

Solve the following equation for x and provide an exact solution:

7^2x + 2(7^x) = 48

Determine the inverse of f(x) = e^{2x -15}. Also, provide the domain and range of the inverse.

Given the equation y = 26(1.8)^x, rewrite the equation in terms of base e and evaluate (to three decimal places).