document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1016064>Question 1016064</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the domain of the function below?<BR>\n" );
document.write( "f(x)=3log base 5(2x+6)-6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #632504 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=632504\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe the only requirement here is that the expression that you are taking the log of must be greater than 0.\r<BR>\n" );
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document.write( "that means that 2x+6 must be greater than 0.\r<BR>\n" );
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document.write( "solve for x to get x has to be greater than -3.\r<BR>\n" );
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document.write( "if you graph this equation, you will see that the value of x can't be less than or equal to -3.\r<BR>\n" );
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document.write( "in other words, it has to be greater than -3.\r<BR>\n" );
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document.write( "the graph is shown below:\r<BR>\n" );
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document.write( "see below the graph for further comments.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/012702.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "from the graph, you can see that the line of the equation approaches x = -3 but will never touch it.\r<BR>\n" );
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document.write( "going to the right, the graph has no end.\r<BR>\n" );
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document.write( "the domain is therefore all real values of x such that x > -3.\r<BR>\n" );
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document.write( "in interval notation that would be x = (-3,infinity)\r<BR>\n" );
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document.write( "x can't be -3 because x = -3 would make the expression inside the log equal to 0 which it can't be.\r<BR>\n" );
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document.write( "x can't be infinity because infinity is not a number.<BR>\n" );
document.write( "it's an expression that says that the right side of the graph goes on forever and has no end.\r<BR>\n" );
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document.write( "you can test this out by just supplying some number to your calculator.\r<BR>\n" );
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document.write( "in order to use the calculator, you need to convert the base of the log to base of 10 or base of e.\r<BR>\n" );
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document.write( "base of 10 is the log function of your calculator.<BR>\n" );
document.write( "base of e is the ln function of your calculator.\r<BR>\n" );
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document.write( "log5(2x+6) would be entered as log(2x+6)/log(5) in your calculator.\r<BR>\n" );
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document.write( "log5(2x+6) can also be entered as ln(2x+6)/ln(5) in your calculator.\r<BR>\n" );
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document.write( "either one will allow your calculator to determine the value of log5(x).\r<BR>\n" );
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document.write( "we'll use the log function as an example.\r<BR>\n" );
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document.write( "3log5(2x+6)-6 would be entered as 3*log(2x+6)/log(5) - 6.\r<BR>\n" );
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document.write( "if your calculator can't handle entering 2x+6 as such, you would need to calculate the value of 2x+6 based on the value of x that you choose, and enter it that way.\r<BR>\n" );
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document.write( "when x = -3, this becomes 3*log(0)/log(5)-6, because 2*-3+6  -6+6 = 0.\r<BR>\n" );
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document.write( "enter that in your calculator and you get something that says you can't do that.\r<BR>\n" );
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document.write( "in my calculator (ti-84 plus), i enter 3*log(0)/log(5)-6 and get ERR:DOMAIN\r<BR>\n" );
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document.write( "it's a little cryptic but it means that i can't take the log of 0.\r<BR>\n" );
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document.write( "if i want to find the log of a positive number, i would do the same.\r<BR>\n" );
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document.write( "when x = 5 in my equation, the expression of 3 * log5(2x+6) - 6 becomes 3 * log5(16) - 6 which i would then enter as 3*log(16)/log(5)-6 and it would tell me that the answer is -.83188.\r<BR>\n" );
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document.write( "look on the graph and you will see that when x = 5, the value of the equation tells you the same thing.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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