document.write( "Question 1183047: 8^x-2 = 2/25, find x \n" ); document.write( "

Algebra.Com's Answer #813197 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "8^x-2 = 2/25, find x
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\n" ); document.write( "\n" ); document.write( " Simpler solution is possible.\r
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document.write( "Your starting equation is\r\n" );
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document.write( "     = .\r\n" );
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document.write( "It is equivalent to\r\n" );
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document.write( "     = .\r\n" );
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document.write( "Take logarithm base 10 of both sides\r\n" );
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document.write( "    3*(x-2)*log(2) = 3*log(2) - 2\r\n" );
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document.write( "Simplify\r\n" );
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document.write( "    (3x - 6)*log(2) = 3*log(2) - 2\r\n" );
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document.write( "    (3x - 6 - 3)*log(2) = -2\r\n" );
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document.write( "    (3x - 9)*log(2) = -2\r\n" );
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document.write( "     3x - 9 = - \r\n" );
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document.write( "     3x     = -  + 9\r\n" );
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document.write( "      x     = -  + 3 = 0.785381  (approximately; rounded).    ANSWER\r\n" );
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document.write( "CHECK.  The left side of the original equation is   = 0.080000 =  = .    ! Correct !\r\n" );
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