SOLUTION: How do I solve for a varaible with a decimal exponent? x^0.725 = 41.494

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Question 230622: How do I solve for a varaible with a decimal exponent?
x^0.725 = 41.494
Answer by jsmallt9(3759) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E0.725+=+41.494
Since the goal is to have an equation that says:
x = some number
Since the exponent on x is 1, we can look at the problem as: "How do I change an exponent of 0.725 to a 1?" One way we could do this is to raise both sides to the 1/0.725 power. Let's see:
%28x%5E0.725%29%5E%281%2F0.725%29+=+%2841.494%29%5E%281%2F0.725%29
The left side works out to be x because
  • %28a%5Eb%29%5Ec+=+a%5E%28bc%29
  • 0.725 and 1/0.725 are reciprocals
  • When you multiply reciprocals you always get 1
  • x%5E1+=+x

So we have
x+=+%2841.494%29%5E%281%2F0.725%29
We can use our calculators to find the right side. (It works out to be approximately 170.4919451462086020.)