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Mathematics - Trigonometric Equations - Solutions

Solve for x
1.) 2^(x-5)=3
I know the answer is: log(base 2) of 3 +5 or 5+(ln3/ln2) but I can't figure out how to get it

2.) lnx+ln(x-1)=1
Answer: (1+square root(1+4e))/2 (Don't understand how to get that)

3.) Simplify the expression tan(inverse sinx)
Answer: x/(sqaure root(1-x^2)) (Don't know how to do)

4.) Find tan(inverse sec(4))
Answer: square root of 15 (Don't know how to do)

5.) f(x)= ln(2+lnx), find domain of f(x)
Answer: (e^(-2), infinity) Don't know how to do it

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Solutions to posted problems which belong to Trigonometric Equations are solved with step by step instruction and given in the attached solution file.