document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=160200>Question 160200</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3log x = log125\r<BR>\n" );
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document.write( "Here is another one I can not find a practice problem like it. <BR>\n" );
document.write( "Thank you in advance for your help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #118159 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=118159\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> here's what i think.<BR>\n" );
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document.write( "log 125 without telling you what the base is implies the base is 10.<BR>\n" );
document.write( "making that assumption, i went to the calculator and found the log of 125.<BR>\n" );
document.write( "it is 2.096910013<BR>\n" );
document.write( "if log (125) = y, and log(125) = 2.096910013, then y = 2.096910013.<BR>\n" );
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document.write( "i looked at the other equation of 3*log(x) and again assumed base of 10.<BR>\n" );
document.write( "the basic properties of logarithms state that 3*log(x) is the same as log (x^3).<BR>\n" );
document.write( "your equation then becomes log(x^3) = log(125) = 2.096910013 = y.<BR>\n" );
document.write( "the basic properties of logarithms also state that y = log(x) if and only if 10^y = x.<BR>\n" );
document.write( "this means that y = log(x^3) if and only if 10^y = x^3.<BR>\n" );
document.write( "since y = 2.096910013, then the equation becomes<BR>\n" );
document.write( "10^(2.096910013) = x^3.<BR>\n" );
document.write( "since 10^(2.096910013) = 125, the equation becomes<BR>\n" );
document.write( "125 = x^3<BR>\n" );
document.write( "since cube root of (125) is 5, then<BR>\n" );
document.write( "x = 5<BR>\n" );
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document.write( "substituting for x in the original equation of 3*log(x) = log(125), we get<BR>\n" );
document.write( "3*log(5) = log(125)<BR>\n" );
document.write( "log(5) = .698970004<BR>\n" );
document.write( "log(125) = 2.096910013<BR>\n" );
document.write( "substituting for log(5) and log(125), the equation becomes<BR>\n" );
document.write( "3*.698970004 = 2.096910013<BR>\n" );
document.write( "this becomes 2.096910013 = 2.096910013<BR>\n" );
document.write( "answer checks out<BR>\n" );
document.write( "3*log(5) = log(125)<BR>\n" );
document.write( "x = 5<BR>\n" );
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document.write( "keys to solving this were:<BR>\n" );
document.write( "1.  know that log without specifying the base assumes a base of 10.<BR>\n" );
document.write( "2.  know that 3*log(x) = log(x^3)<BR>\n" );
document.write( "3.  know that y = log(x) if and only if 10^y = x<BR>\n" );
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document.write( "another way of looking at this that might have been even simpler.<BR>\n" );
document.write( "it's pretty logical actually.<BR>\n" );
document.write( "i'm not sure if it works in all cases but it worked in this one.<BR>\n" );
document.write( "it goes as follows:<BR>\n" );
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document.write( "if log(a) = log(b) then a must = b<BR>\n" );
document.write( "this probably would work with any base, not just 10, as long as the base on the left side of the equation is the same as the base on the right side of the equation.<BR>\n" );
document.write( "correspondingly, if log(a^3) = log (b) then a^3 must = b<BR>\n" );
document.write( "that would have led directly to x^3 = 125 from the original equation.<BR>\n" );
document.write( "you would have had to know, at least, that 3*log(x) = log(x^3).<BR>\n" );
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document.write( "both ways lead to the same answer, at least in this case.<BR>\n" );
document.write( " </SPAN>\n" );
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