find the domain of the function f(x)=log(x-2).

Question

1. find the domain of the function f(x)=log(x-2).

 

2. evaluate log8^4 analytically.

 

3. use a graphing utility to solve the equation e^-x=3 lnx

Answer 1

1. The argument to log must be positive so the domain of f(x) = log(x-2) is x > 2

 

2. log₈ 4 = log₈ 64^1/3 = (1/3)log₈ 64 = (1/3)log₈ 8² = (1/3)·2 = 2/3

 

3. There are many utilities available for this. TI calculators have one for numeric equation solving. I used an online utility called Wolfram|Alpha with the following command:

 

solve e^-x = 3 lnx

 

It gives the solution x ≈ 1.11545