document.write( "Question 1116083: What is the inverse function of:\r
\n" ); document.write( "\n" ); document.write( "f(x) = (1/2)^x \n" ); document.write( "

Algebra.Com's Answer #730915 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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What is the inverse function of:
\n" ); document.write( " $\"f%28x%29+=+%281%2F2%29%5Ex\"$
\n" ); document.write( "y = f(x)
\n" ); document.write( " $\"y+=+%281%2F2%29%5Ex\"$
\n" ); document.write( "Swap x and y, solve for y
\n" ); document.write( " $\"x+=+%281%2F2%29%5Ey\"$
\n" ); document.write( "Find the y root of both sides
\n" ); document.write( " $\"x%5E%281%2Fy%29+=+1%2F2\"$
\n" ); document.write( "Using common logs
\n" ); document.write( " $\"log%28%28x%5E%281%2Fy%29%29%29+=+log%28%281%2F2%29%29\"$
\n" ); document.write( "the log equiv of exponents
\n" ); document.write( " $\"%281%2Fy%29log%28%28x%29%29+=+log%28%281%2F2%29%29\"$
\n" ); document.write( "multiply both sides by y
\n" ); document.write( " $\"log%28%28x%29%29+=+y%2Alog%28%281%2F2%29%29\"$
\n" ); document.write( "divide both sides by log(1/2)
\n" ); document.write( " $\"log%28%28x%29%29%2Flog%28%281%2F2%29%29\"$ = y
\n" ); document.write( ":\r
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\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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