SOLUTION: If 5^x = √ 5^195+5^195+5^195+5^195+5^195, then what is the value of x?

Algebra ->  Square-cubic-other-roots -> SOLUTION: If 5^x = √ 5^195+5^195+5^195+5^195+5^195, then what is the value of x?      Log On


   

Question 1138691: If 5^x = √ 5^195+5^195+5^195+5^195+5^195, then what is the value of x?
Found 3 solutions by greenestamps, MathTherapy, MathLover1:
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


5%5E195%2B5%5E195%2B5%5E195%2B5%5E195%2B5%5E195+=+5%285%5E195%29+=+5%5E196+=+5%5Ex
x+=+196

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Oops! forgot what the original problem was....

sqrt%285%5E196%29+=+5%5E98+=+5%5Ex

x = 98

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
If 5^x = √ 5^195+5^195+5^195+5^195+5^195, then what is the value of x?


matrix%281%2C3%2C+5%5Ex%2C+%22=%22%2C+sqrt%285%285%5E195%29%29%29

matrix%281%2C3%2C+5%5Ex%2C+%22=%22%2C+sqrt%285%5E196%29%29%29 

matrix%281%2C3%2C+%285%5Ex%29%5E2%2C+%22=%22%2C+%28sqrt%285%5E196%29%29%5E2%29 ------- Squaring each side

matrix%281%2C3%2C+5%5E%282x%29%2C+%22=%22%2C+5%5E196%29

2x = 196 ------ Bases are equal and so are the exponents

highlight_green%28matrix%281%2C5%2C+x%2C+%22=%22%2C+196%2F2%2C+%22=%22%2C+98%29%29

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

if you have
5%5Ex+=+sqrt%285%5E195+%2B+5%5E195+%2B+5%5E195+%2B+5%5E195+%2B+5%5E195%29
5%5Ex+=+sqrt%285%2A5%5E195%29
5%5Ex+=+sqrt%285%5E196%29
5%5Ex+=+%285%5E196%29%5E%281%2F2%29
5%5Ex+=+5%5E%28196%2F2%29
5%5Ex+=+5%5E98...if bases same, we have
x+=98