document.write( "Question 1130719: 10^4logx - 7(10^2logx) + 10 = 0 \n" ); document.write( "

Algebra.Com's Answer #747367 by ikleyn(52814) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " Much more shorter and straightforward solution is possible.\r
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document.write( "First, since \"x\" is under the logarithm function, it must be positive: x > 0.\r\n" );
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document.write( "So, the domain for this equation is the set {x | x > 0 }.\r\n" );
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document.write( "Second,   = x;  therefore, the original equation in the domain  x > 0  is equivalent to this simple equation\r\n" );
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document.write( " = 0.\r\n" );
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document.write( "Factor left side:\r\n" );
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document.write( "(x^2-5)*(x^2-2) = 0.\r\n" );
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document.write( "Formally, it has  4 solutions  ,  ,    and  .\r\n" );
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document.write( "Of these, only positive numbers belong to the domain, so the answer is these two numbers    and  .\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "Regarding the post by @MathLover1, notice that the negative $\"-sqrt%285%29\"$ and $\"-sqrt%282%29\"$ are not the solutions.\r
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\n" ); document.write( "\n" ); document.write( "To count them among the solutions, as @MathLover1 does, is a rude mistake.\r
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\n" ); document.write( "\n" ); document.write( "The way on how @MathLover1 solves the problem is ANTIPEDAGOGIC.\r
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\n" ); document.write( "\n" ); document.write( "When the student presents the solution in this way, he (or she) simply demonstrates that he (or she)
\n" ); document.write( "does not know the basic properties of logarithms.\r
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\n" ); document.write( "\n" ); document.write( "The lesson to learn from my solution is THIS :\r
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document.write( "    the problem in the post is designed and intended to be solved in the way as presented.\r\n" );
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\n" ); document.write( "\n" ); document.write( "I don't know for what reason the tutor @greenestamps kicks me and my solution, which is absolutely correct.\r
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\n" ); document.write( "\n" ); document.write( "Simply ignore/disregard his post in the part which relates to my solution.\r
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\n" ); document.write( "\n" ); document.write( "In the future, to avoid misunderstanding and ambiguity, write your formulas using parentheses like this:\r
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\n" ); document.write( "\n" ); document.write( "10^(4*logx) - 7*(10^(2*logx)) + 10 = 0.\r
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\n" ); document.write( "\n" ); document.write( "It is the plain text format, which is uniquely appropriate format for posting to this forum.\r
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\n" ); document.write( "\n" ); document.write( "It corresponds to this form of the equation\r
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\n" ); document.write( "\n" ); document.write( " $\"10%5E%284%2Alogx%29\"$ - $\"7%2A%2810%5E%282%2Alogx%29%29\"$ + $\"10\"$ = 0.\r
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