document.write( "Question 1191994: 8x=2^(x-2) solve x \n" ); document.write( "

Algebra.Com's Answer #823873 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "In general, this kind of equation, with one term a constant times the variable and another term with the variable in an exponent, can't be solved algebraically; you need to use a graphing calculator, or calculus or some other numerical method.

\n" ); document.write( "But this particular problem can be solved easily, because the answer is \"nice\".

\n" ); document.write( "We can tell that the equation will have a \"nice\" answer only if the value of the variable is an integer; if not, we would not be able to evaluate 2^(x-2) exactly.

\n" ); document.write( "So simply try small integer values for x to find the answer.

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document.write( "  x  x-2  8x  2^(x-2)\r\n" );
document.write( " --------------------\r\n" );
document.write( "  3   1   24    2\r\n" );
document.write( "  4   2   32    4\r\n" );
document.write( "  5   3   40    8\r\n" );
document.write( "  6   4   48   16\r\n" );
document.write( "  7   5   56   32\r\n" );
document.write( "  8   6   64   64

\n" ); document.write( "ANSWER: x=8

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