document.write( "Question 905391: log(6x-3)base 3=1+log(x-3)base3) \n" ); document.write( "

Algebra.Com's Answer #853538 by MathTherapy(10699) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "log(6x-3)base 3=1+log(x-3)base3)\r\n" );
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document.write( "What the other person who responded, says (see below), is TOTALLY FALSE!! His/Her answer is also WRONG, so IGNORE it all!!\r\n" );
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document.write( "WRONG!! WRONG!! WRONG!!\r\n" );
document.write( "Since the bases of the logs are the same (number 3 in this case), then the insides must be equal. That is:\r\n" );
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document.write( "6x - 3 = 1 + x - 3\r\n" );
document.write( "6x - x = 3 - 3 + 1\r\n" );
document.write( "5x = 1\r\n" );
document.write( "x = 1/5\r\n" );
document.write( "Understand?\r\n" );
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document.write( "Notice that there is a 1 ATTACHED to the log on the right! \r\n" );
document.write( "Anyway, the smaller variable-expression, x - 3, MUST be > 0. We then get: x - 3 > 0, and x > 3. The problem then becomes:\r\n" );
document.write( ", with the constraint, x > 3.\r\n" );
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document.write( "          ---- Applying  = \r\n" );
document.write( "                 --- Converting to EXPONENTIAL form             \r\n" );
document.write( "                6x - 3 = 3(x - 3) ----- Cross-multiplying\r\n" );
document.write( "                6x - 3 = 3x - 9 \r\n" );
document.write( "               6x - 3x = - 9 + 3\r\n" );
document.write( "                    3x = - 6\r\n" );
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document.write( "However, x = - 2 is NOT a solution, as it is NOT > 3, which makes this x-value, EXTRANEOUS!. So, there are NO SOLUTIONS!

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