SOLUTION: What is the value of a if 7^a-7^a-5= 117642√7?

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Question 1148139: What is the value of a if 7^a-7^a-5= 117642√7?
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


Please think about when parentheses are needed when you type algebraic expressions.

Clearly you mean 7^a-7^(a-5), which is , instead of 7^a-7^a-5, which is , which is just -5.

On the left, factor out a common factor of 7^(a-5):



On the right, using the prime factorization of 117642 or any other method, determine that

Then we have



from which we can obtain



So




ANSWER: a = 6.5, or 13/2


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