document.write( "Question 394648: 1. 4^x+6(4^-x)=5
\n" ); document.write( "2. 5(5^2x)+8(5^x)=6 \n" ); document.write( "

Algebra.Com's Answer #279979 by lwsshak3(11628) $\"\"$ $\"About$

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1. 4^x+6(4^-x)=5
\n" ); document.write( "2. 5(5^2x)+8(5^x)=6\r
\n" ); document.write( "\n" ); document.write( "solving first problem
\n" ); document.write( "4^x+6(4^-x)=5
\n" ); document.write( "4^x+6(1/4^x)=5
\n" ); document.write( "multiply by LCD 4^x
\n" ); document.write( "4^2x+6=5(4^x)
\n" ); document.write( "4^2x-5(4^x)+6=0
\n" ); document.write( "let 4^x = u
\n" ); document.write( "then u^2 =4^2x
\n" ); document.write( "u^2-5u+6=0
\n" ); document.write( "factor to solve
\n" ); document.write( "(u-3)(u-2)=0
\n" ); document.write( "u=3, u=2\r
\n" ); document.write( "\n" ); document.write( "4^x=3
\n" ); document.write( "xlog4=log3
\n" ); document.write( "x=log3/log4=.79248\r
\n" ); document.write( "\n" ); document.write( "4^x=2
\n" ); document.write( "xlog4=log2
\n" ); document.write( "x=log2/log4=.5000\r
\n" ); document.write( "\n" ); document.write( "answers: x=.79248 or .5
\n" ); document.write( "check: 4^x+6(4^-x)=5
\n" ); document.write( "f(.79248)=4^.79428+6*(1/4^.79248)
\n" ); document.write( " =3.00749+2.00000 = 5.00749\r
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\n" ); document.write( "\n" ); document.write( "Solving second problem
\n" ); document.write( "5(5^2x)+8(5^x)=6
\n" ); document.write( "let u=5^x
\n" ); document.write( "then u^2 =5^2x
\n" ); document.write( "5u^2+8u-6=0
\n" ); document.write( "Use following quadratic formula to solve
\n" ); document.write( "with a=5, b=8,c=-6
\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "u=(-8+-sqrt(8^2-4*5*-6))/10
\n" ); document.write( " =(-8+-sqrt(184))/10
\n" ); document.write( " =(-8+-13.5646)/10
\n" ); document.write( " =-21.5646/10 or 5.5646/10
\n" ); document.write( " =-2.15646 or .55646\r
\n" ); document.write( "\n" ); document.write( "5^x=-2.15646 (reject,no solution,(5^x)>0
\n" ); document.write( "5^x=.55646
\n" ); document.write( "xlog5=log.55646
\n" ); document.write( " x=log.55646/log5
\n" ); document.write( " ans: x=-.36420
\n" ); document.write( "check:
\n" ); document.write( "5(5^2x)+8(5^x)=6
\n" ); document.write( "1.54824+4.45169 =5.99993\r
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