document.write( "Question 146747This question is from textbook Advanced Functions and Introductory Caculus
\n" ); document.write( ": Find algebraic solutions for each system of equation\r
\n" ); document.write( "\n" ); document.write( "b) y= 2(1/3)^(-x) and y=6(9)^(x+1)\r
\n" ); document.write( "\n" ); document.write( "c) y= 1000(0.1)^(2x) and y=10^x\r
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\n" ); document.write( "\n" ); document.write( "thank you! \n" ); document.write( "
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b)\r
\n" ); document.write( "\n" ); document.write( "y=2(3)^x
\n" ); document.write( "y=6(9)(9)^x\r
\n" ); document.write( "\n" ); document.write( "So we want\r
\n" ); document.write( "\n" ); document.write( "2(3)^x=6(9)(9)^x
\n" ); document.write( "3^x=3(3^2)(3)^(2x)
\n" ); document.write( "3^x=3^(2x+3)\r
\n" ); document.write( "\n" ); document.write( "so x=2x+3
\n" ); document.write( "-3=x.
\n" ); document.write( "And y becomes y=2(3)^(-3)=2/27\r
\n" ); document.write( "\n" ); document.write( "c.
\n" ); document.write( "y=1000(.1)^(2x)
\n" ); document.write( "y=10^x\r
\n" ); document.write( "\n" ); document.write( "so we want
\n" ); document.write( "1000(.1)^(2x)=10^x
\n" ); document.write( "10^3(10^(-1))^(2x)=10^x
\n" ); document.write( "10^(-2x+3)=10^x\r
\n" ); document.write( "\n" ); document.write( "so -2x+3=x
\n" ); document.write( "and x=1
\n" ); document.write( "y becomes 10.\r
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