document.write( "Question 712630: Find the exact solution, using common logarithms:
\n" ); document.write( "5^x+125(5^-x)=30 \n" ); document.write( "

Algebra.Com's Answer #438097 by josgarithmetic(39630) $\"\"$ $\"About$

You can put this solution on YOUR website!
Common logarithms not necessary, pointless. See how this solution works:\r
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\n" ); document.write( "\n" ); document.write( " $\"5%5Ex%2B125%285%5E%28-x%29%29=30\"$ , as given.
\n" ); document.write( " $\"5%5Ex%2B125%2F%285%5Ex%29-30=0\"$
\n" ); document.write( "Multiply both sides by 5^x.
\n" ); document.write( " $\"%285%5Ex%295%5Ex%2B125%2A%285%5Ex%29%285%5E%28-x%29%29-30%2A5%5Ex=0%2A5%5Ex\"$
\n" ); document.write( " $\"5%5E%282x%29-30%2A5%5Ex%2B125=0\"$ , which is factorable.
\n" ); document.write( " $\"highlight%28%285%5Ex-5%29%285%5Ex-25%29=0%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Taking $\"5%5Ex-5=0\"$ , 5^x=5, $\"x=1\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Taking $\"5%5Ex-25=0\"$ , 5^x=25, 5^x=5^2, $\"x=2\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Answer: $\"highlight%28x=1%29\"$ or $\"highlight%28x=2%29\"$ . \n" ); document.write( "

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