document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=170951>Question 170951</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0970999526/algebrahomeworkh>LOF Advanced Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Please show the step-by-step solution to:<BR>\n" );
document.write( "Prove [(log7)4][log4)9]= [(log7)9] <BR>\n" );
document.write( "Textbook hint: start by dividing each side by [(log7)4].....\r<BR>\n" );
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document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #126215 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=126215\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's one way to do it:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28log%287%2C%284%29%29%29%28log%284%2C%289%29%29%29=log%287%2C%289%29%29 ALIGN=MIDDLE  ALT=\"%28log%287%2C%284%29%29%29%28log%284%2C%289%29%29%29=log%287%2C%289%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation. Note: I'm ONLY going to manipulate the left side. The right side is for comparison\r<BR>\n" );
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document.write( "By the change of base formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28x%29%29=log%2810%2C%28x%29%29%2Flog%2810%2C%28b%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28x%29%29=log%2810%2C%28x%29%29%2Flog%2810%2C%28b%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%287%2C%284%29%29 ALIGN=MIDDLE  ALT=\"log%287%2C%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28log%2810%2C%284%29%29%29%2F%28log%2810%2C%287%29%29%29 ALIGN=MIDDLE  ALT=\"%28log%2810%2C%284%29%29%29%2F%28log%2810%2C%287%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Also, we can rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284%2C%289%29%29 ALIGN=MIDDLE  ALT=\"log%284%2C%289%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28log%2810%2C%289%29%29%29%2F%28log%2810%2C%284%29%29%29 ALIGN=MIDDLE  ALT=\"%28log%2810%2C%289%29%29%29%2F%28log%2810%2C%284%29%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=%28%28log%2810%2C%284%29%29%29%2F%28log%2810%2C%287%29%29%29%29%28%28log%2810%2C%289%29%29%29%2F%28log%2810%2C%284%29%29%29%29=log%287%2C%289%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Use the change of base formula to expand the logarithms (see above)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28highlight%28log%2810%2C%284%29%29%29%2F%28log%2810%2C%287%29%29%29%29%28%28log%2810%2C%289%29%29%29%2Fhighlight%28log%2810%2C%284%29%29%29%29=log%287%2C%289%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Highlight the common terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%28log%2810%2C%284%29%29%29%2F%28log%2810%2C%287%29%29%29%29%28%28log%2810%2C%289%29%29%29%2Fcross%28log%2810%2C%284%29%29%29%29=log%287%2C%289%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Cancel out the common terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%28log%2810%2C%287%29%29%29%29%28%28log%2810%2C%287%29%29%29%2F1%29=log%287%2C%289%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28log%2810%2C%287%29%29%29%2F%28log%2810%2C%287%29%29%29%29=log%287%2C%289%29%29 ALIGN=MIDDLE  ALT=\"%28%28log%2810%2C%287%29%29%29%2F%28log%2810%2C%287%29%29%29%29=log%287%2C%289%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine and multiply the fractions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%287%2C%289%29%29=log%287%2C%289%29%29 ALIGN=MIDDLE  ALT=\"log%287%2C%289%29%29=log%287%2C%289%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the change of base formula (in reverse) to simplify the left side\r<BR>\n" );
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document.write( "So this shows us that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28log%287%2C%284%29%29%29%28log%284%2C%289%29%29%29=log%287%2C%289%29%29 ALIGN=MIDDLE  ALT=\"%28log%287%2C%284%29%29%29%28log%284%2C%289%29%29%29=log%287%2C%289%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note: this can be generalized to say that \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28log%28x%2C%28y%29%29%29%28log%28y%2C%28z%29%29%29=log%28x%2C%28z%29%29 ALIGN=MIDDLE  ALT=\"%28log%28x%2C%28y%29%29%29%28log%28y%2C%28z%29%29%29=log%28x%2C%28z%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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