document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=20542>Question 20542</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4log<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + log<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >5 = log<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >405 What is the value of X in this logarithm? When I tried to work it I simplified the equation to log<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >x^4 + log<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >5 = log<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >405. Then I subtracted x from both sides and was left with log<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >x^4 = 400. Please walk me through this because even if I am doing it correctly I don't know what to do next.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #9895 by </B><A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><B>AnlytcPhil(1806)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><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=AnlytcPhil><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=9895\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 4log<sub>2</sub>x + log<sub>2</sub>5 = log<sub>2</sub>405 What is the value of x in this logarithm? When I tried<BR>\n" );
document.write( "to work it I simplified the equation to log<sub>2</sub>x<sup>4</sup> + log<sub>2</sub>5 = log<sub>2</sub>405. Then I<BR>\n" );
document.write( "subtracted x from both sides and was left with  = 400. Please walk me through<BR>\n" );
document.write( "this because even if I am doing it correctly I don't know what to do next.<BR>\n" );
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document.write( "One error was in thinking log<sub>2</sub>405 - log<sub>2</sub>5 = log<sub>2</sub>(405-5) = log<sub>2</sub>(400).  This is<BR>\n" );
document.write( "wrong.  The rule is<BR>\n" );
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document.write( "log<sub>B</sub>U - log<sub>B</sub>V = log<sub>B</sub>(U/V)<BR>\n" );
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document.write( "[NOT log<sub>B</sub>(U-V)]<BR>\n" );
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document.write( "So you should have gotten log<sub>2</sub>405 - log<sub>2</sub>5 = log<sub>2</sub>(405/5) = log<sub>2</sub>(81).<BR>\n" );
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document.write( "This would have simplified to<BR>\n" );
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document.write( "x<sup>4</sup> = 81<BR>\n" );
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document.write( "which you could have solved and gotten x = ±3 and then discarded the -3 since<BR>\n" );
document.write( "logs cannot be taken of negative numbers.<BR>\n" );
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document.write( "However. also always try, if possible, to avoid using the rule N·log<sub>B</sub>X = log<sub>B</sub>X<sup>N</sup><BR>\n" );
document.write( "whenever it causes variables to be raised to higher powers.  You can often<BR>\n" );
document.write( "avoid this by dividing through by the value of N.<BR>\n" );
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document.write( "4log<sub>2</sub>x + log<sub>2</sub>5 = log<sub>2</sub>405  <BR>\n" );
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document.write( "Subtract log<sub>2</sub>5 from both sides<BR>\n" );
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document.write( "4log<sub>2</sub>x = log<sub>2</sub>405 - log<sub>2</sub>5<BR>\n" );
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document.write( "Use the rule log<sub></sub>U - log<sub>B</sub>V = log<sub>B</sub>(U/V) on the right<BR>\n" );
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document.write( "4log<sub>2</sub>x = log<sub>2</sub>(405/5)<BR>\n" );
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document.write( "4log<sub>2</sub>x = log<sub>2</sub>(81)<BR>\n" );
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document.write( "Here is where you want to avoid using the rule N·log<sub>B</sub>X = log<sub>B</sub>X<sup>N</sup>, to avoid<BR>\n" );
document.write( "causing the variable x to be raised to the fourth power. Let's work on the right<BR>\n" );
document.write( "side some more instead, noting that 81 = 3<sup>4</sup>.<BR>\n" );
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document.write( "4log<sub>2</sub>x = log<sub>2</sub>(3<sup>4</sup>)<BR>\n" );
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document.write( "Now we can use log<sub>B</sub>X<sup>N</sup> = N·log<sub>B</sub>X on the right sides<BR>\n" );
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document.write( "4log<sub>2</sub>x = 4log<sub>2</sub>3<BR>\n" );
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document.write( "Now we can divide both sides by 4.<BR>\n" );
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document.write( "log<sub>2</sub>x = log<sub>2</sub>3<BR>\n" );
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document.write( "Raise both sides to the 2nd power, which is the same as dropping the log<sub>2</sub>'s,<BR>\n" );
document.write( "and we get<BR>\n" );
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document.write( "x = 3  <BR>\n" );
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document.write( "Edwin<BR>\n" );
document.write( "AnlytcPhil@aol.com\r<BR>\n" );
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