document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=606283>Question 606283</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use common or natural logarithms to solve the exponential equation symbolically.<BR>\n" );
document.write( "4^(7-3x)=1/16 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #382001 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=382001\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 4^{\left(7\ -\ 3x\right)}\ =\ \frac{1}{16}\">\r<BR>\n" );
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document.write( "The trick here is to note that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{1}{16}\ =\ 4^{-2}\">\r<BR>\n" );
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document.write( "Then you can write:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 4^{\left(7\ -\ 3x\right)}\ =\ 4^{-2}\">\r<BR>\n" );
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document.write( "Now you really don't have to actually mess with taking the log of both sides.  Since the bases are equal you can simply equate the exponents.  But in the interest of never being so stupid as to not follow your math teacher's instructions, herewith the logarithm way.  I use natural logs but you can use any base you like and the result will be the same.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ln\left(4^{\left(7\ -\ 3x\right)}\right)\ =\ \ln\left(4^{-2}\right)\">\r<BR>\n" );
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document.write( "Then use\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \log_b(x^n)\ =\ n\log_b(x)\">\r<BR>\n" );
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document.write( "to write:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(7\ -\ 3x\right)\ln\left(4\right) \ =\ -2\ln\left(4\right)\">\r<BR>\n" );
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document.write( "Then divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ln(4)\">  (Do you see why <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \log_b(4)\"> would have worked regardless of the value of the logarithm base?)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 7\ -\ 3x\ =\ -2\">\r<BR>\n" );
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document.write( "Just solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\">.  Don't forget to check your answer.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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