document.write( "Question 1171189: Pls help me solve this equation (0.25)=16,5^2x-26(5^x)+25=0 \n" ); document.write( "
Algebra.Com's Answer #796105 by ikleyn(52781)\"\" \"About 
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document.write( "5^(2x) - 26*5^x + 25 = 0\r\n" );
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document.write( "\"5%5E%282x%29+-+26%2A5%5Ex+%2B+25+=+0\"\r\n" );
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document.write( "Introduce new variable  u = \"5%5Ex\".\r\n" );
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document.write( "Then the equation takes the form\r\n" );
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document.write( "    u^2 - 26u + 25 = 0.\r\n" );
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document.write( "Factor left side\r\n" );
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document.write( "    (u-25)*(u-1) = 0.\r\n" );
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document.write( "The roots of this equation are  u= 25  and  u= 1.\r\n" );
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document.write( "If u= 25,  then  \"5%5Ex\" = 25 = \"5%5E2\";  hence,  x = 2.\r\n" );
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document.write( "If u=  1,  then  \"5%5Ex\" =  1 = \"5%5E0\";  hence,  x = 0.\r\n" );
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document.write( "ANSWER.  The original equation has two solutions:  x= 0  and  x= 2.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Introducing new variable is a standard method for solving such equations.\r
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\n" ); document.write( "\n" ); document.write( "To see numerous examples of solving exponential equations, look into the lessons \r
\n" ); document.write( "\n" ); document.write( "    - Solving exponential equations\r
\n" ); document.write( "\n" ); document.write( "    - Solving advanced exponential equations\r
\n" ); document.write( "\n" ); document.write( "    - OVERVIEW of lessons on 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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