document.write( "Question 202241: Which one of the following is true? (1) log(7+3)=log7+log3 (2) (log10)^3=3log10 (3) ln(7e^10)=10+ln7 ? HELP. \n" ); document.write( "

Algebra.Com's Answer #852443 by ikleyn(52925) $\"\"$ $\"About$

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\n" ); document.write( "Which one of the following is true?
\n" ); document.write( "(1) log(7+3)=log7+log3
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\n" ); document.write( "(3) ln(7e^10)=10+ln7 ? HELP.
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\n" ); document.write( "\n" ); document.write( "        The answers in the post by @Theo are incorrect.\r
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\n" ); document.write( "\n" ); document.write( "        His writing is so confusing that it is difficult to comment on.\r
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\n" ); document.write( "\n" ); document.write( "        I came to bring correct answers.\r
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document.write( "Question (1).  Left side is  log(10) = 1.\r\n" );
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document.write( "               Right side, due to the logarithm rules,  is log(7*3) = log(21).\r\n" );
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document.write( "               log(10) and log(21) are different expressions, not identical and not equal.\r\n" );
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document.write( "               Hence, formula (1) is wrong.\r\n" );
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document.write( "Question (2).  Left side is  (log(10))^3 = 1^3 = 1.\r\n" );
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document.write( "               Right side is  3log(10) = 3*1 = 3.\r\n" );
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document.write( "               Thus, left side and right side represent different numbers,\r\n" );
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document.write( "               so, formula (2) is wrong.\r\n" );
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document.write( "Question (3).  Left side is  ln(7) + ln(e^10) = ln(7) + 10.\r\n" );
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document.write( "               Right side is 10 + ln(7), which is the same as  ln(7) + 10.\r\n" );
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document.write( "               So, we conclude that formula (3) is correct.\r\n" );
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document.write( "ANSWER.  Of the three formulas, only (3) is true.  Others are wrong.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "Ignore the post by @Theo for the peace in your mind.\r
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