document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=99359>Question 99359</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Evaluate log6 (36) without using your calculator. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #72270 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=72270\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%2C36%29 ALIGN=MIDDLE  ALT=\"log%286%2C36%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "To evaluate this, let's say that it equals y. So we write the problem as:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%2C36%29+=+y ALIGN=MIDDLE  ALT=\"log%286%2C36%29+=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "In your head, you can change this to exponential form by raising the base 6 to the y power and<BR>\n" );
document.write( "setting it equal to 36. In equation form this is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%5Ey+=+36 ALIGN=MIDDLE  ALT=\"6%5Ey+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "But you can recognize that 36 is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%5E2 ALIGN=MIDDLE  ALT=\"6%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So substitute this for 36 and the equation<BR>\n" );
document.write( "becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%5Ey+=+6%5E2 ALIGN=MIDDLE  ALT=\"6%5Ey+=+6%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now notice that on both sides of this equation the base number is 6 and it is raised to<BR>\n" );
document.write( "a power. Since the power is 2 on one side and y on the other side, the value of y has to<BR>\n" );
document.write( "be 2 if both sides are equal. Therefore, you have found that y must be equal to 2. <BR>\n" );
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document.write( "Next recall that way back at the beginning we said that:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%2C36%29+=+y ALIGN=MIDDLE  ALT=\"log%286%2C36%29+=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So you can substitute 2 for y and get the answer:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%2C36%29+=+2 ALIGN=MIDDLE  ALT=\"log%286%2C36%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "Hope this helps you to see how you can do the problem without using a calculator. <BR>\n" );
document.write( "(Most calculators don't work for logarithm bases other than 10 or e anyhow unless you<BR>\n" );
document.write( "use a formula known as the \"change of base formula.\")<BR>\n" );
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document.write( "The technique for changing from logarithmic form to exponential form is very useful in<BR>\n" );
document.write( "solving many logarithmic problems. You should become proficient in using it.<BR>\n" );
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document.write( " </SPAN>\n" );
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