Science:Math Exam Resources/Courses/MATH110/December 2013/Question 06 (a)
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Question 06 (a) 

Consider the function: (a) How many solutions are there to the equation ? Justify your answer. 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Simplifying the enumerator first might help. Remember the rule for the product of exponentials: 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. We first simplify using the exponential rules to get Then we can solve for .
By taking the natural logarithm of both sides, we get a on the right hand side which is bad since is not in the domain of the natural logarithm. So we conclude that there cannot be a solution to the equation . Hence, we have solutions. 