SOLUTION: How can I solve this? Find x. 1. (64) raise to x = 8 2. ([the square root of 49]) raise to 1/2 = x 3. 1/16 = 16 raise to x

Algebra ->  Algebra  -> Square-cubic-other-roots -> SOLUTION: How can I solve this? Find x. 1. (64) raise to x = 8 2. ([the square root of 49]) raise to 1/2 = x 3. 1/16 = 16 raise to x      Log On

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Question 11161: How can I solve this? Find x.
1. (64) raise to x = 8
2. ([the square root of 49]) raise to 1/2 = x
3. 1/16 = 16 raise to x
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
1. 64%5Ex+=+8, well short of doing logs or knowing the answer by looking, as i would expect someone who is 17-18 years old to do (i have no idea how old you are), then do the following:

%282%5E6%29%5Ex+=+2%5E3
2%5E%286x%29+=+2%5E3

so, the two sides are equal, so 6x = 3, so x = 1/2.

2. %28sqrt%2849%29%29%5E%281%2F2%29+=+x

x+=+%28%2B7%29%5E%281%2F2%29 or x+=+%28-7%29%5E%281%2F2%29

x+=+%2Bsqrt%287%29 or x+=+-sqrt%287%29 or x+=+%2Bsqrt%28-7%29 or x+=+-sqrt%28-7%29
x+=+%2Bsqrt%287%29 or x+=+-sqrt%287%29 or x+=+%2Bsqrt%287%2A%28-1%29%29 or x+=+-sqrt%287%2A%28-1%29%29
x+=+%2Bsqrt%287%29 or x+=+-sqrt%287%29 or x+=+%2Bsqrt%287%29sqrt%28-1%29 or x+=+-sqrt%287%29sqrt%28-1%29
x+=+%2Bsqrt%287%29 or x+=+-sqrt%287%29 or x+=+%2Bsqrt%287%29i or x+=+-sqrt%287%29i.

3. 1%2F16+=+16%5Ex
16%5E%28-1%29+=+16%5Ex

again, equating the 2 sides gives x = -1.

jon.