document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=320194>Question 320194</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1) Solve for m:          2 log (3m) = 2\r<BR>\n" );
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document.write( "2) Find the exact value of sin e if cot e = 5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #229350 by </B><A HREF=/tutors/aboutme.mpl?userid=nyc_function><B>nyc_function(2741)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nyc_function><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=nyc_function><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=229350\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For question 1, we use the fact that y = log_b (x) if and only if b^(y) = x.\r<BR>\n" );
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document.write( "Let b = 10^2\r<BR>\n" );
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document.write( "Let x = (3m)^2\r<BR>\n" );
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document.write( "We now have the following equation:\r<BR>\n" );
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document.write( "10^2 = (3m)^2\r<BR>\n" );
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document.write( "100 = 9m^2\r<BR>\n" );
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document.write( "100/9 = m^2\r<BR>\n" );
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document.write( "11.11111111 = m^2\r<BR>\n" );
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document.write( "Take square root of both sides.\r<BR>\n" );
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document.write( "sqrt{11.11111111} = sqrt{m^2}\r<BR>\n" );
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document.write( "3.3333333333 = m\r<BR>\n" );
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document.write( "The decimal number 3.333333333 can be written as 10/3 as the value of m.\r<BR>\n" );
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document.write( "Did you follow?\r<BR>\n" );
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document.write( "========================================================================\r<BR>\n" );
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document.write( "For the trig question, the first thing to notice is that sine and cotagent are both positive, which means we are in quadrant 1.\r<BR>\n" );
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document.write( "We are in quadrant 1 using a right triangle to find the hypotenuse via the famous Pythagorean Theorem.\r<BR>\n" );
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document.write( "cot(e) = 5 = 5/1\r<BR>\n" );
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document.write( "sin(e) = 1/(hyp)\r<BR>\n" );
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document.write( "Also keep in mind:\r<BR>\n" );
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document.write( "cotangent = adj/opp\r<BR>\n" );
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document.write( "sine = opp/hyp\r<BR>\n" );
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document.write( "We need to find the hypotenuse of the right triangle formed in quadrant 1.\r<BR>\n" );
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document.write( "1^2 + 5^2 = (hyp)^2\r<BR>\n" );
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document.write( "26 = (hyp)^2\r<BR>\n" );
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document.write( "We now take the square root of both sides.\r<BR>\n" );
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document.write( "sqrt{26} = sqrt{(hyp)^2}\r<BR>\n" );
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document.write( "sqrt{26} = hypotenuse\r<BR>\n" );
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document.write( "Are you with me so far?\r<BR>\n" );
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document.write( "==========================================\r<BR>\n" );
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document.write( "Since we now know the value of the hypotenuse, we can plug that into<BR>\n" );
document.write( "sin(e) = 1/(hyp), which becomes sin(e) = 1/sqrt{26}.\r<BR>\n" );
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document.write( "It is never a good idea to leave a radical in the denominator of a fraction.\r<BR>\n" );
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document.write( "We now need to rationalize the denominator.  This is done to remove the radical from the denominator.\r<BR>\n" );
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document.write( "To do so, multiply the TOP and BOTTOM by the sqrt{26}.\r<BR>\n" );
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document.write( "sin(e) = 1/sqrt{26} times [sqrt{26}/sqrt{26}]\r<BR>\n" );
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document.write( "sin(e) = sqrt{26}/26\r<BR>\n" );
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document.write( "Did you follow?\r<BR>\n" );
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document.write( " </SPAN>\n" );
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