document.write( "Question 177704: what is the value of x?
\n" ); document.write( "4^20+4^20=2^x \n" ); document.write( "

Algebra.Com's Answer #132726 by EMStelley(208) $\"\"$ $\"About$

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To solve this problem you need to be a little clever. The first thing to notice is that everything on the left hand side is a power of 4 while everything on the right hand side is a power of 2. It would be nice if they were the same, specifically 2, since that's the side with the variable. Can we change $\"4%5E20\"$ into base 2? Sure, since $\"4=2%5E2\"$ . So we have that
\n" ); document.write( " $\"%282%5E2%29%5E20=4%5E20\"$
\n" ); document.write( "And because of the rules of exponents, we have that
\n" ); document.write( " $\"2%5E40=4%5E20\"$
\n" ); document.write( "So we can rewrite the equation:
\n" ); document.write( " $\"2%5E40%2B2%5E40=2%5Ex\"$
\n" ); document.write( "Now, we combine like terms on the left hand side:
\n" ); document.write( " $\"2%282%5E40%29=2%5Ex\"$
\n" ); document.write( "What is $\"2%282%5E40%29\"$ ? Well, all we're doing is multiplying by another 2, so it's just $\"2%5E41\"$ . So,
\n" ); document.write( " $\"2%5E41=2%5Ex\"$
\n" ); document.write( "So x=41. \n" ); document.write( "

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