document.write( "Question 1065221: The following logarithm problem is a catastrophe. I did it three times and was hoping for same answer, but nope. Every time I got a different answer. \r
\n" ); document.write( "\n" ); document.write( "TRY 1:\r
\n" ); document.write( "\n" ); document.write( "log_b( 28 ) - log_b(7X) = log_b( 8 )\r
\n" ); document.write( "\n" ); document.write( "log_b( 28/7 )=log_b( 8 )\r
\n" ); document.write( "\n" ); document.write( "log_b( 4/x )=log_b( 8 )\r
\n" ); document.write( "\n" ); document.write( "log_b( 4 )-log_b( x )-log_b( 8 )=0\r
\n" ); document.write( "\n" ); document.write( "log_b( 4 )-log_b( 8 )=log_b( x )\r
\n" ); document.write( "\n" ); document.write( "log_b( x )=log_b( 4 )-log_b( 8 )\r
\n" ); document.write( "\n" ); document.write( "Now, I am gonna raise b to each side to get rid of log_b\r
\n" ); document.write( "\n" ); document.write( "b^(log_b( x ))=b^(log_b( 4 ))-b^(log_b( 8 ))\r
\n" ); document.write( "\n" ); document.write( "x=4-8= -4\r
\n" ); document.write( "\n" ); document.write( "This solution is incorrect, and I am not sure why. I think I did everything right to the best of my knowledge. \r
\n" ); document.write( "\n" ); document.write( "TRY 2:\r
\n" ); document.write( "\n" ); document.write( "log_b( 28 )-log_b( 7X )=log_b( 8 )\r
\n" ); document.write( "\n" ); document.write( "log_b( 28 )-log_b( 8 )=log_b( 7X )\r
\n" ); document.write( "\n" ); document.write( "Now, I am raising b to each side to get rid of log_b\r
\n" ); document.write( "\n" ); document.write( "b^(log_b( 28 ))-b^(log_b( 8 ))=b^(log_b( 7X ))\r
\n" ); document.write( "\n" ); document.write( "28-8=7x\r
\n" ); document.write( "\n" ); document.write( "20/7=x\r
\n" ); document.write( "\n" ); document.write( "This solution is also wrong, and I am not sure why, but to me, everything looks fine. \r
\n" ); document.write( "\n" ); document.write( "TRY 3 (the one COPIED from the book):\r
\n" ); document.write( "\n" ); document.write( "log_b( 4/x )=log_b( 8 )\r
\n" ); document.write( "\n" ); document.write( "Now, I am raising b to each side to get rid of log_b\r
\n" ); document.write( "\n" ); document.write( "b^log_b( 4/x )=b^(log_b( 8 ))\r
\n" ); document.write( "\n" ); document.write( "4/x=8\r
\n" ); document.write( "\n" ); document.write( "4=8x\r
\n" ); document.write( "\n" ); document.write( "4/8=x\r
\n" ); document.write( "\n" ); document.write( "1/2=x\r
\n" ); document.write( "\n" ); document.write( "This solution is correct. I understand how it's derived, but I have no clue why the above two solutions are not the same than this one. I expected them to be the same regardless of how I solve the problem. \r
\n" ); document.write( "\n" ); document.write( "Thank you for having the courage to answer this long question. \n" ); document.write( "
Algebra.Com's Answer #680346 by MathTherapy(10552)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "The following logarithm problem is a catastrophe. I did it three times and was hoping for same answer, but nope. Every time I got a different answer. \r\n" );
document.write( "\r\n" );
document.write( "TRY 1:\r\n" );
document.write( "log_b( 28 ) - log_b(7X) = log_b( 8 )\r\n" );
document.write( "log_b( 28/7 )=log_b( 8 )\r\n" );
document.write( "log_b( 4/x )=log_b( 8 )\r\n" );
document.write( "log_b( 4 )-log_b( x )-log_b( 8 )=0\r\n" );
document.write( "log_b( 4 )-log_b( 8 )=log_b( x )\r\n" );
document.write( "log_b( x )=log_b( 4 )-log_b( 8 )\r\n" );
document.write( "Now, I am gonna raise b to each side to get rid of log_b\r\n" );
document.write( "b^(log_b( x ))=b^(log_b( 4 ))-b^(log_b( 8 ))\r\n" );
document.write( "x=4-8= -4\r\n" );
document.write( "\r\n" );
document.write( "This solution is incorrect, and I am not sure why. I think I did everything right to the best of my knowledge. \r\n" );
document.write( "\r\n" );
document.write( "TRY 2:\r\n" );
document.write( "log_b( 28 )-log_b( 7X )=log_b( 8 )\r\n" );
document.write( "log_b( 28 )-log_b( 8 )=log_b( 7X )\r\n" );
document.write( "Now, I am raising b to each side to get rid of log_b\r\n" );
document.write( "b^(log_b( 28 ))-b^(log_b( 8 ))=b^(log_b( 7X ))\r\n" );
document.write( "28-8=7x\r\n" );
document.write( "20/7=x\r\n" );
document.write( "\r\n" );
document.write( "This solution is also wrong, and I am not sure why, but to me, everything looks fine. \r\n" );
document.write( "\r\n" );
document.write( "TRY 3 (the one COPIED from the book):\r\n" );
document.write( "log_b( 4/x )=log_b( 8 )\r\n" );
document.write( "Now, I am raising b to each side to get rid of log_b\r\n" );
document.write( "b^log_b( 4/x )=b^(log_b( 8 ))\r\n" );
document.write( "4/x=8\r\n" );
document.write( "4=8x\r\n" );
document.write( "4/8=x\r\n" );
document.write( "1/2=x\r\n" );
document.write( "\r\n" );
document.write( "This solution is correct. I understand how it's derived, but I have no clue why the above two solutions are not the same than this one. I expected them to be the same regardless of how I solve the problem. \r\n" );
document.write( "Thank you for having the courage to answer this long question.\r\n" );
document.write( "\r\n" );
document.write( "The following logarithm problem is a catastrophe. I did it three times and was hoping for same answer, but nope. Every time I got a different answer.

\n" ); document.write( "
TRY 1:\r\n" );
document.write( "log_b( 28 ) - log_b(7X) = log_b( 8 )\r\n" );
document.write( "log_b( 28/7 )=log_b( 8 ) This should be \"28%2F%287x%29\" \r\n" );
document.write( "log_b( 4/x )=log_b( 8 )  You are correct up to here\r\n" );
document.write( "\r\n" );
document.write( "log_b( 4 )-log_b( x )-log_b( 8 )=0\r\n" );
document.write( "log_b( 4 )-log_b( 8 )=log_b( x )\r\n" );
document.write( "log_b( x )=log_b( 4 )-log_b( 8 )\r\n" );
document.write( "Now, I am gonna raise b to each side to get rid of log_b\r\n" );
document.write( "b^(log_b( x ))=b^(log_b( 4 ))-b^(log_b( 8 ))\r\n" );
document.write( "x=4-8= -4\r\n" );
document.write( "\r\n" );
document.write( "log_b( 4/x )=log_b( 8 ) Picking up where you were last correct\r\n" );
document.write( "\"4%2Fx+=+8\" ------ \"log+%28a%2C+%28d%2Fe%29%29+=+log+%28a%2C+%28f%29%29\" means that: \"d%2Fe+=+f\"\r\n" );
document.write( "Continue solving for x and you should get: \"x+=+1%2F2\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "TRY 2:\r\n" );
document.write( "log_b( 28 )-log_b( 7X )=log_b( 8 )\r\n" );
document.write( "log_b( 28 )-log_b( 8 )=log_b( 7X ) You are correct up to here\r\n" );
document.write( " \r\n" );
document.write( "Now, I am raising b to each side to get rid of log_b\r\n" );
document.write( "b^(log_b( 28 ))-b^(log_b( 8 ))=b^(log_b( 7X ))\r\n" );
document.write( "28-8=7x\r\n" );
document.write( "20/7=x\r\n" );
document.write( "\r\n" );
document.write( "log_b( 28 )-log_b( 8 )=log_b( 7X ) Picking up where you were last correct\r\n" );
document.write( "\"log+%28b%2C+%2828%2F8%29%29+=+log+%28b%2C+%287x%29%29\" \r\n" );
document.write( "\"28%2F8+=+7x\" ------ AGAIN, \"log+%28a%2C+%28d%2Fe%29%29+=+log+%28a%2C+%28f%29%29\" means that: \"d%2Fe+=+f\"\r\n" );
document.write( "\"7%2F2+=+7x\" ------- Reducing fraction on left side\r\n" );
document.write( "14x = 7 ------ Cross-multiplying\r\n" );
document.write( "\"matrix%281%2C5%2C+x%2C+%22=%22%2C+7%2F14%2C+or%2C+1%2F2%29\"\r\n" );
document.write( "\r\n" );
document.write( "There you go....same answer!
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