document.write( "Question 1209710: 4^(1/√x) + 16^(1/√x) = 64^(1/√x)
\n" ); document.write( "find x, \n" ); document.write( "

Algebra.Com's Answer #849950 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The exponents are all the same, so let's simplify the equation.

\n" ); document.write( " $\"a=1%2Fsqrt%28x%29\"$
\n" ); document.write( " $\"4%5Ea%2B16%5Ea=64%5Ea\"$

\n" ); document.write( "16=4^2 and 4=4^3, so

\n" ); document.write( " $\"b=4%5Ea\"$
\n" ); document.write( " $\"b%2Bb%5E2=b%5E3\"$
\n" ); document.write( " $\"b%5E3-b%5E2-b=0\"$
\n" ); document.write( " $\"b%28b%5E2-b-1%29=0\"$

\n" ); document.write( "The solutions for b are 0, $\"%281%2Bsqrt%285%29%29%2F2\"$ , and $\"%281-sqrt%285%29%29%2F2\"$

\n" ); document.write( "Since b=4^a, the first and third values for b are not possible, so $\"b=%281%2Bsqrt%285%29%29%2F2\"$

\n" ); document.write( "Then

\n" ); document.write( " $\"4%5Ea=%281%2Bsqrt%285%29%29%2F2\"$

\n" ); document.write( " $\"4%5E%281%2Fsqrt%28x%29%29=%281%2Bsqrt%285%29%29%2F2\"$

\n" ); document.write( " $\"%281%2Fsqrt%28x%29%29%2Alog%284%29=log%28%281%2Bsqrt%285%29%2F2%29%29%29\"$

\n" ); document.write( " $\"x=%28log%284%29%2Flog%28%281%2Bsqrt%285%29%2F2%29%29%29%5E2\"$

\n" ); document.write( "Evaluating that expression using a calculator gives...

\n" ); document.write( "ANSWER: x = 8.29924014....

\n" ); document.write( " \n" ); document.write( "

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