document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1102963>Question 1102963</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The apparent magnitude of a star refers to the brightness of the star. Objects with lower magnitude appear brighter to the eye than objects with higher magnitude. For higher magnitudes a telescope is required. However, even a telescope has its limitations. The limiting magnitude L of an optical telescope with lens diameter D (in inches) is given by L(D) = 8.8 + 5.1logD. Use this function to find the following: <BR>\n" );
document.write( "a. Find the limiting magnitude for a telescope with a lens 10 inches in diameter. Round to 1 decimal place if needed. <BR>\n" );
document.write( "b. How large a telescope is needed to see a galaxy with magnitude 19? Round to the nearest inch if needed. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #717723 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=717723\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The apparent magnitude of a star refers to the brightness of the star. <BR>\n" );
document.write( "Objects with lower magnitude appear brighter to the eye than objects with higher magnitude.<BR>\n" );
document.write( " For higher magnitudes a telescope is required.<BR>\n" );
document.write( " However, even a telescope has its limitations. <BR>\n" );
document.write( "The limiting magnitude L of an optical telescope with lens diameter D (in inches) is given by L(D) = 8.8 + 5.1logD.<BR>\n" );
document.write( " Use this function to find the following:<BR>\n" );
document.write( ": <BR>\n" );
document.write( "a. Find the limiting magnitude for a telescope with a lens 10 inches in diameter.<BR>\n" );
document.write( " Round to 1 decimal place if needed.<BR>\n" );
document.write( "L(d) = 5.1*log(10)<BR>\n" );
document.write( "We know the log of 10 is 1, therefore<BR>\n" );
document.write( "L = 5.1 amplitude<BR>\n" );
document.write( ": <BR>\n" );
document.write( "b. How large a telescope is needed to see a galaxy with magnitude 19?<BR>\n" );
document.write( " Round to the nearest inch if needed.<BR>\n" );
document.write( "5.1*log(d) = 19<BR>\n" );
document.write( "log(d) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19%2F5.1 ALIGN=MIDDLE  ALT=\"19%2F5.1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "log(d) = 3.7255<BR>\n" );
document.write( "Find the antilog<BR>\n" );
document.write( "d = 5315 inches or divide by 12 to get 443 ft <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );