document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=295955>Question 295955</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, what is the log of log7 50=<BR>\n" );
document.write( "Sorry, I am not sure how to make the 7 a subscript.\r<BR>\n" );
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document.write( "I understand I am trying to find the exponent of 7 that will produce 50.  <BR>\n" );
document.write( "7 squared is 49, so what do I do from there?\r<BR>\n" );
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document.write( "Thanking You in Advance,<BR>\n" );
document.write( "Jacinta\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #213320 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=213320\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your equation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%287%2C50%29+=+y ALIGN=MIDDLE  ALT=\"log%287%2C50%29+=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This is true, if and only if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%5Ey+=+50 ALIGN=MIDDLE  ALT=\"7%5Ey+=+50\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Take the log of both sides of this equation to get:\r<BR>\n" );
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document.write( "this log you are taking is to the base 10 which is the LOG function of your calculator.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C7%5Ey%29+=+log%2810%2C50%29 ALIGN=MIDDLE  ALT=\"log%2810%2C7%5Ey%29+=+log%2810%2C50%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since, in general, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28x%5Ey%29+=+y%2Alog%28x%29 ALIGN=MIDDLE  ALT=\"log%28x%5Ey%29+=+y%2Alog%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this equation becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2Alog%2810%2C7%29+=+log%2810%2C50%29 ALIGN=MIDDLE  ALT=\"y%2Alog%2810%2C7%29+=+log%2810%2C50%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide both sides of this equation by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C7%29 ALIGN=MIDDLE  ALT=\"log%2810%2C7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+log%2810%2C50%29%2Flog%2810%2C7%29 ALIGN=MIDDLE  ALT=\"y+=+log%2810%2C50%29%2Flog%2810%2C7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ***** \r<BR>\n" );
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document.write( "***** This equation is the log base conversion formula described below.\r<BR>\n" );
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document.write( "Use your calculator to get log of 50 divided by log of 10 to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+1.698970004%2F.84509804 ALIGN=MIDDLE  ALT=\"y+=+1.698970004%2F.84509804\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2.010382138 ALIGN=MIDDLE  ALT=\"y+=+2.010382138\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "That's your answer:\r<BR>\n" );
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document.write( "Plug into your original equation to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%287%2C50%29+=+y ALIGN=MIDDLE  ALT=\"log%287%2C50%29+=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%287%2C50%29+=+2.010382138 ALIGN=MIDDLE  ALT=\"log%287%2C50%29+=+2.010382138\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "this is true if and only if:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%5E2.010382138+=+50 ALIGN=MIDDLE  ALT=\"7%5E2.010382138+=+50\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Use your calculator to determine that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%5E2.010382138 ALIGN=MIDDLE  ALT=\"7%5E2.010382138\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 50, confirming that the answer of y = 2.010382138 is good.\r<BR>\n" );
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document.write( "You needed to know that, in general:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2Cx%29+=+y ALIGN=MIDDLE  ALT=\"log%28b%2Cx%29+=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" > if and only if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5Ey+=+x ALIGN=MIDDLE  ALT=\"b%5Ey+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "There is also a log base conversion formula that will provide you with the same answer.\r<BR>\n" );
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document.write( "That conversion formula is:\r<BR>\n" );
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document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2Cx%29+=+log%28c%2Cx%29+%2F+log%28c%2Cb%29 ALIGN=MIDDLE  ALT=\"log%28b%2Cx%29+=+log%28c%2Cx%29+%2F+log%28c%2Cb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In your case, this conversion formula would work like this:\r<BR>\n" );
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document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%287%2C50%29+=+log%2810%2C50%29+%2F+log%2810%2C7%29 ALIGN=MIDDLE  ALT=\"log%287%2C50%29+=+log%2810%2C50%29+%2F+log%2810%2C7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If you look at what we did earlier, you will see that our solution yielded this exact formula.\r<BR>\n" );
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document.write( "That would be the equation denoted with ***** up above.\r<BR>\n" );
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document.write( "That equation was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+log%2810%2C50%29%2Flog%2810%2C7%29 ALIGN=MIDDLE  ALT=\"y+=+log%2810%2C50%29%2Flog%2810%2C7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Our conversion equation here is:\r<BR>\n" );
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document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%287%2C50%29+=+log%2810%2C50%29+%2F+log%2810%2C7%29 ALIGN=MIDDLE  ALT=\"log%287%2C50%29+=+log%2810%2C50%29+%2F+log%2810%2C7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%287%2C50%29 ALIGN=MIDDLE  ALT=\"log%287%2C50%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is your original equation.\r<BR>\n" );
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document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C50%29+%2F+log%2810%2C7%29 ALIGN=MIDDLE  ALT=\"log%2810%2C50%29+%2F+log%2810%2C7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the conversion equation.\r<BR>\n" );
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