document.write( "Question 639939: Solve the exponential equation. 6^x-48*6^-x=2. What is the exact solution. What is the decimal approximation for the solution. Show all work. \n" ); document.write( "

Algebra.Com's Answer #402934 by Alan3354(69443) $\"\"$ $\"About$

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6^x-48*6^-x=2
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\n" ); document.write( " $\"6%5Ex+-+48%2A6%5E%28-x%29+=+2\"$
\n" ); document.write( "Multiply by 6^x
\n" ); document.write( " $\"6%5E%282x%29+-+48+=+2%2A6%5Ex\"$
\n" ); document.write( "Sub y for 6^x
\n" ); document.write( " $\"y%5E2+-+48+=+2y\"$
\n" ); document.write( " $\"y%5E2+-+2y+-+48+=+0\"$
\n" ); document.write( "(y-8)*(y+6) = 0
\n" ); document.write( "y = -6 --> 6^x = -6 not allowed.
\n" ); document.write( "-----------
\n" ); document.write( "y = 8 --> 6^x = 8
\n" ); document.write( "x*log(6) = log(8)
\n" ); document.write( "x = log(8)/log(6)
\n" ); document.write( "or $\"x+=+log%286%2C8%29\"$
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\n" ); document.write( "x =~ 1.160558
\n" ); document.write( "=================
\n" ); document.write( "After doing this, I see I could have made it simpler:
\n" ); document.write( " $\"6%5Ex+-+48%2A6%5E%28-x%29+=+2\"$
\n" ); document.write( "Sub y here
\n" ); document.write( "y - (48/y) = 2
\n" ); document.write( "etc
\n" ); document.write( " \n" ); document.write( "

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