document.write( "Question 954792: Solve log2(x-2)-log2(x+5)=3 \n" ); document.write( "

Algebra.Com's Answer #854134 by MathTherapy(10801) $\"\"$ $\"About$

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document.write( "Solve log2(x-2)-log2(x+5)=3\r\n" );
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document.write( "The solution, x = - 6, by the other person who responded, is WRONG!! \r\n" );
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document.write( "The SMALLER of the 2 log arguments, x - 2 MUST be > 0. So, x - 2 > 0 ===> x > 2.\r\n" );
document.write( "We then have: , with x > 2.\r\n" );
document.write( "                                            ----- Applying  = \r\n" );
document.write( "                                                        ---- Converting to EXPONENTIAL form \r\n" );
document.write( "                                                       \r\n" );
document.write( "                                                   8(x + 5) = x - 2 ----- Cross-multiplying \r\n" );
document.write( "                                                    8x + 40 = x - 2 \r\n" );
document.write( "                                                        8x - x = - 2 - 40\r\n" );
document.write( "                                                              7x = - 42                                                                                                 \r\n" );
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document.write( "The x-value, - 6, is NOT > 2, and is therefore an EXTRANEOUS solution, which makes it an INVALID/UNACCEPTABLE solution. \r\n" );
document.write( "So, this equation DOESN'T have a solution!!

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