document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=149457>Question 149457</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321356918/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The instructions say for each function, find f^-1. Help please, step by step.  Thank you...\r<BR>\n" );
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document.write( "f(x)= 6^x-1\r<BR>\n" );
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document.write( "Also, solve each equation. Find the Exact solutions.\r<BR>\n" );
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document.write( "1/2^x = 5    the exponent is above the 2 only. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #109646 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=109646\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=+6%5E%28x-1%29+ ALIGN=MIDDLE  ALT=\"f%28x%29=+6%5E%28x-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given function.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+6%5E%28f%28x%29-1%29+ ALIGN=MIDDLE  ALT=\"x=+6%5E%28f%28x%29-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Switch x and f(x).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%28x%29%29=+log%2810%2C%286%5E%28f%28x%29-1%29%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%28x%29%29=+log%2810%2C%286%5E%28f%28x%29-1%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the log of both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%28x%29%29=+%28f%28x%29-1%29%2Alog%2810%2C%286%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%28x%29%29=+%28f%28x%29-1%29%2Alog%2810%2C%286%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite the right side using the identity  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%28x%29%29=+f%28x%29%2Alog%2810%2C%286%29%29-log%2810%2C%286%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%28x%29%29=+f%28x%29%2Alog%2810%2C%286%29%29-log%2810%2C%286%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%28x%29%29%2Blog%2810%2C%286%29%29=+f%28x%29%2Alog%2810%2C%286%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%28x%29%29%2Blog%2810%2C%286%29%29=+f%28x%29%2Alog%2810%2C%286%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%286%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%286%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%286x%29%29=+f%28x%29%2Alog%2810%2C%286%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%286x%29%29=+f%28x%29%2Alog%2810%2C%286%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the logs using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28A%29%29%2Blog%28b%2C%28B%29%29=log%28b%2C%28A%2AB%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28A%29%29%2Blog%28b%2C%28B%29%29=log%28b%2C%28A%2AB%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%286x%29%29%2Flog%2810%2C%286%29%29=+f%28x%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%286x%29%29%2Flog%2810%2C%286%29%29=+f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%286%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%286%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate f(x)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%2C%286x%29%29=+f%28x%29 ALIGN=MIDDLE  ALT=\"log%286%2C%286x%29%29=+f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the change of base formula to rewrite the left side.\r<BR>\n" );
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document.write( "So the inverse function is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f^{-1}\left(x\right)=\log_{6}\left(6x\right)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%29%2F%282%5Ex%29+=+5 ALIGN=MIDDLE  ALT=\"%281%29%2F%282%5Ex%29+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=+5%282%5Ex%29 ALIGN=MIDDLE  ALT=\"1=+5%282%5Ex%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Ex ALIGN=MIDDLE  ALT=\"2%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F5=2%5Ex ALIGN=MIDDLE  ALT=\"1%2F5=2%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%281%2F5%29%29=log%2810%2C%282%5Ex%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%281%2F5%29%29=log%2810%2C%282%5Ex%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Take the log of both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%281%2F5%29%29=x%2Alog%2810%2C%282%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%281%2F5%29%29=x%2Alog%2810%2C%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Rewrite the right side using the identity  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%281%2F5%29%29%2Flog%2810%2C%282%29%29=x ALIGN=MIDDLE  ALT=\"log%2810%2C%281%2F5%29%29%2Flog%2810%2C%282%29%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%282%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%281%2F5%29%29=x ALIGN=MIDDLE  ALT=\"log%282%2C%281%2F5%29%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the change of base formula to rewrite the left side.\r<BR>\n" );
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document.write( "So the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=log%282%2C%281%2F5%29%29 ALIGN=MIDDLE  ALT=\"x=log%282%2C%281%2F5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which approximates to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2.32192 ALIGN=MIDDLE  ALT=\"x=-2.32192\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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