> solve for x and give an exact answer
An exact answer means you can't use a calculator. You must find a simplified expression for x.
Dividing both sides by 5: 2^x = 14 = 2 * 7
Dividing both sides by 2: 2^(x-1) = 7
Taking log's (base 10) of both sides: log(2^(x-1)) = log(7)
Applying exponent rule for logs: (x-1)log2 = log7
Simplifying: x = ((log7)/(log2)) + 1; which is an exact answer.