document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=574198>Question 574198</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that F(x) =log 2 (x+1)-3<BR>\n" );
document.write( "a) what s the domain of F?<BR>\n" );
document.write( "what is F(7)? what point is on the graph of F?<BR>\n" );
document.write( "b) if F(x)=-1, what is x? what point s on the graph of F?<BR>\n" );
document.write( "c)What is the zero of F\r<BR>\n" );
document.write( "\n" );
document.write( "please explain me or show me how should I do b, and c, i do know how to do a.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #369033 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=369033\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F%28x%29+=log%28+2%2C+%28x%2B1%29%29-3 ALIGN=MIDDLE  ALT=\"F%28x%29+=log%28+2%2C+%28x%2B1%29%29-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b) F(x) = -1<BR>\n" );
document.write( "Substitute the given value for F(x):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1+=log%28+2%2C+%28x%2B1%29%29-3 ALIGN=MIDDLE  ALT=\"-1+=log%28+2%2C+%28x%2B1%29%29-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now solve for x.<br><BR>\n" );
document.write( "To solve for x in an equation like this we usually start by transforming the equation into one of the following forms:<BR>\n" );
document.write( "log(expression) = other_expression<BR>\n" );
document.write( "or<BR>\n" );
document.write( "log(expression) = log(other_expression)<br><BR>\n" );
document.write( "Since your equation has only a single log in it, we will aim for the first form. All we have to do to add three to each side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+=log%28+2%2C+%28x%2B1%29%29 ALIGN=MIDDLE  ALT=\"2+=log%28+2%2C+%28x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "With the equation in the first form, then next step is to rewrite the equation in exponential form. In general, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28a%2C+%28p%29%29+=+q ALIGN=MIDDLE  ALT=\"log%28a%2C+%28p%29%29+=+q\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Eq+=+p ALIGN=MIDDLE  ALT=\"a%5Eq+=+p\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Using this pattern on your equation we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E2+=+x%2B1 ALIGN=MIDDLE  ALT=\"2%5E2+=+x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies to:<BR>\n" );
document.write( "4 = x + 1<br><BR>\n" );
document.write( "With the logarithm now gone the equation is simple to solve, Just subtract 1 from each side:<BR>\n" );
document.write( "3 = x<br><BR>\n" );
document.write( "When solving equations like<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1+=log%28+2%2C+%28x%2B1%29%29-3 ALIGN=MIDDLE  ALT=\"-1+=log%28+2%2C+%28x%2B1%29%29-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "it is important, <i>not optional</i>, to check your answer! You have to ensure that all arguments (and bases) remain valid (i.e. positive). Checking x = 3:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1+=log%28+2%2C+%283%2B1%29%29-3 ALIGN=MIDDLE  ALT=\"-1+=log%28+2%2C+%283%2B1%29%29-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We can quickly see that the only log's argument is 4. And its base is 2. These are both valid/allowable numbers so the required part of the check is complete.<br><BR>\n" );
document.write( "So F(3) = -1 which means the point (3, -1) is a point on the graph of F(x).<br><BR>\n" );
document.write( "c) Find the zeros. This just means find the x value or values where the function's value is zero. IOW: Find all x's such that F(x) = 0. Solve this just like part b (using 0, instead of -1 of course).<BR>\n" );
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