document.write( "Question 356236: 4^3x-2^3x= 20 what is the value of x \n" ); document.write( "

Algebra.Com's Answer #254289 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"4%5E%283x%29-2%5E%283x%29=+20+\"$
\n" ); document.write( " $\"%282%5E2%29%5E%283x%29-2%5E%283x%29=20\"$
\n" ); document.write( " $\"2%5E%286x%29-2%5E%283x%29-20=0\"$
\n" ); document.write( "Use a substitution, let $\"u=2%5E%283x%29\"$ , then $\"u%5E2=2%5E%286x%29\"$
\n" ); document.write( " $\"u%5E2-u-20=0\"$
\n" ); document.write( " $\"%28u-5%29%28u%2B4%29=0\"$
\n" ); document.write( "Two solutions in u:
\n" ); document.write( " $\"u-5=0\"$
\n" ); document.write( " $\"u=5\"$
\n" ); document.write( " $\"2%5E%283x%29=5\"$
\n" ); document.write( " $\"3x=log%282%2C%285%29%29\"$
\n" ); document.write( " $\"x=%281%2F3%29log%282%2C%285%29%29\"$
\n" ); document.write( " $\"x=%281%2F3%29%28log%28%285%29%29%2Flog%28%282%29%29%29\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"u%2B4=0\"$
\n" ); document.write( " $\"u=-4\"$
\n" ); document.write( " $\"2%5E%283x%29=-4\"$
\n" ); document.write( "No power of 2 will give a negative answer.
\n" ); document.write( "No solution from this u value.
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"x=%281%2F3%29%28log%28%285%29%29%2Flog%28%282%29%29%29\"$ \n" ); document.write( "

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