document.write( "Question 1111408: 5^x − 45(5^−x) + 4 = 0
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Algebra.Com's Answer #726410 by ikleyn(52802) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "Answer. x = 1.\r
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document.write( "Introduce new variable u = .\r\n" );
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document.write( "Then your equation takes the form\r\n" );
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document.write( "u  - 45/u + 4 = 0,\r\n" );
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document.write( "u^2 + 4u - 45 = 0,\r\n" );
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document.write( "(u-5)*(u+9) = 0\r\n" );
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document.write( "The last equation has two roots u= 5 and u= -9,\r\n" );
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document.write( "but since u = ,  only positive \"u\" works.\r\n" );
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document.write( "Thus u = 5,   = 5  and x = 1.\r\n" );
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\n" ); document.write( "Introducing new variable is the STANDARD method of solving exponential equations.\r
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\n" ); document.write( "\n" ); document.write( "See the lesson \r
\n" ); document.write( "\n" ); document.write( " - Solving exponential equations\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( " - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic \"Exponential equations\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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