Eddie S.

asked • 03/24/14

solve(v2)^x=256 for x

learning operations with radicals. no logarithms please.

Kay H.

x=2 and v=8.you can check it by substitution too. (8*2)^2=256
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04/30/14

Parviz F.

√2 = 2^ (1/2)   is conversion of radical to decimal exponent.
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04/30/14

1 Expert Answer

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Parviz F. answered • 03/24/14

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  √2X = 256
 
 
   2X/2 = 256 = 28
 
 
    X/2 = 8
 
 
    X = 16
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Bill V.

 
I am sorry, but in 2^x/2, what is number 2(not 2 in x/2) called please? Thank you.
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03/24/14

Parviz F.

Roots and fractional exponents are equivalent:
 
n√Xn = X      ( Xn ) 1/n = Xn . 1/n = X
 
   In this case √2X= 2 X . 1/2 = 2 x/2
 
   After determining equivalency of roots( radicals) with fractional exponents, then use laws of muliplication
  of exponents , to raise an exponent to another  exponent, multiply exponents together.
 
((a )m ) n  = a mn
 
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03/24/14

Parviz F.

(√2 ) ^X  =
 
(2 ^1/2 ) ^ X =
 
2 ^( X/2)
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04/30/14

Parviz F.

Testing:
 
  (√2 ) ^ 16 = √(2 ^ 16) = (√2 ^ 16 ) = 2 8 = 256
 
 Using Calculator;
√(2 ^ 16) = 256
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04/30/14

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