document.write( "Question 1180949: Express the function in the form f(x) = 5(1/3)^2x-1 in the form f(x) = a•d^-x
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Algebra.Com's Answer #810773 by greenestamps(13200)\"\" \"About 
You can put this solution on YOUR website!


\n" ); document.write( "The function you show is not an exponential function:

\n" ); document.write( "f(x) = 5(1/3)^2x-1 is \"f%28x%29+=+5%281%2F3%29%5E2x-1\"

\n" ); document.write( "It's astonishing to me how few students who post questions about this level of math seem to realize that the proper use of parentheses is important...!

\n" ); document.write( "Nevertheless, there is some good algebra to be learned here; so I will go ahead and work with the function you INTENDED to show.

\n" ); document.write( "f(x) = 5(1/3)^(2x-1) = \"f%28x%29+=+5%281%2F3%29%5E%282x-1%29\"

\n" ); document.write( "We are to write this as an equivalent function in the form \"a%28d%29%5Ex\"

\n" ); document.write( "To do that, we need to get rid of the \"2\" and the \"-1\" in the exponent.

\n" ); document.write( "To get rid of the \"-1\" in the exponent, multiply AND divide the expression by (1/3):

\n" ); document.write( "\"5%2F%281%2F3%29=5%2A3=15\"
\n" ); document.write( "\"%28%281%2F3%29%5E%282x-1%29%29%281%2F3%29=%281%2F3%29%5E%282x%29\"

\n" ); document.write( "The expression is now

\n" ); document.write( "\"15%281%2F3%29%5E%282x%29\"

\n" ); document.write( "To make the exponent x instead of 2x, use the power-to-a-power rule:

\n" ); document.write( "\"15%281%2F3%29%5E%282x%29=15%28%281%2F3%29%5E2%29%5Ex=15%281%2F9%29%5Ex\"

\n" ); document.write( "ANSWER: \"f%28x%29+=+5%281%2F3%29%5E%282x-1%29=15%281%2F9%29%5Ex\"

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