document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=70516>Question 70516</A>: <I><SPAN STYLE=\"word-break: break-all;\"> write the logarithmic equation in exponential form:\r<BR>\n" );
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document.write( "log 3 27 = 3\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "log 125 25 = 2/3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #50301 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=50301\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the log form is log b (d) = c <BR>\n" );
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document.write( "(read that as log to the base b of d equals c) <BR>\n" );
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document.write( "then the corresponding exponential form is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5Ec+=+d ALIGN=MIDDLE  ALT=\"b%5Ec+=+d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You are given log 3 (27) = 3. By comparing this with the log form (see top line above) you can<BR>\n" );
document.write( "see that b = 3, d = 27, and c = 3.  Putting these numbers in the appropriate places in the<BR>\n" );
document.write( "exponential form results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E3+=+27 ALIGN=MIDDLE  ALT=\"3%5E3+=+27\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Note that this equation is true because if you cube 3 you get 27<BR>\n" );
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document.write( "You are also given log 125 (25) = 2/3. By again comparing this with the log form in the first<BR>\n" );
document.write( "line of this reply, you see that b = 125, d = 25, and c = 2/3.  Substituting these numbers <BR>\n" );
document.write( "for their corresponding letters in the exponential form results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=125%5E+%282%2F3%29+=+25 ALIGN=MIDDLE  ALT=\"125%5E+%282%2F3%29+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You may recognize that the exponent <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > means that you can either square the number and<BR>\n" );
document.write( "then take the cube root, or you can take the cube root and then square that number.<BR>\n" );
document.write( "In the case of 125, it is easier to first take the cube root because it is 5, and then<BR>\n" );
document.write( "you square that to get 25.  This means the exponential form is true because the left side<BR>\n" );
document.write( "of that equation equals the right side.<BR>\n" );
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document.write( "If you work a number of these, you will see the pattern between the log and exponential<BR>\n" );
document.write( "forms and the translation back and forth between the two forms will become easier for you.<BR>\n" );
document.write( "Hope this helps you see your way through this type of problem. </SPAN>\n" );
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