document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=284540>Question 284540</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write in terms of the NATURAL LOG. (ln)<BR>\n" );
document.write( "1. log (base 4)x<BR>\n" );
document.write( "2. log (base 10) (x+1)<BR>\n" );
document.write( "3. log (base 5) x^4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #206449 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=206449\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The formula for converting a logarithm of one base into an expression of logarithms of another base is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28a%2C+%28p%29%29+=+log%28b%2C+%28p%29%29%2Flog%28b%2C+%28a%29%29 ALIGN=MIDDLE  ALT=\"log%28a%2C+%28p%29%29+=+log%28b%2C+%28p%29%29%2Flog%28b%2C+%28a%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (Note where the argument and the base of the original logarithm (on the left) end up on the right side.)<br><BR>\n" );
document.write( "We will use this to convert your logarithms into natural logarithms (aka ln). I'll do the last one first because it is harder than the other two.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%285%2C+%28x%5E4%29%29 ALIGN=MIDDLE  ALT=\"log%285%2C+%28x%5E4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using the conversion formula on this we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28x%5E4%29%2Fln%285%29 ALIGN=MIDDLE  ALT=\"ln%28x%5E4%29%2Fln%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This may be an acceptable answer. But we could use a property of logarithms, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28a%2C+%28p%5Eq%29%29+=+q%2Alog%28a%2C+%28p%29%29 ALIGN=MIDDLE  ALT=\"log%28a%2C+%28p%5Eq%29%29+=+q%2Alog%28a%2C+%28p%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to move the exponent of the argument in the numerator out in front:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4ln%28x%29%2Fln%285%29 ALIGN=MIDDLE  ALT=\"4ln%28x%29%2Fln%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The other two problems are just one step. I'll leave them for you to finish. Just use the conversion formula like I did above. </SPAN>\n" );
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