document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=312696>Question 312696</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I do believe this is an exponential equation.  Not sure how to solve using the calculator TI-84 or by hand.  Your help would be appreciated.  Thank you.  TJ \r<BR>\n" );
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document.write( "5*6^4x+3-15=20       the ^ represents the exponent 4x+3 above the 6  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #223567 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=223567\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "I'm presuming you mean:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 5\,\cdot\,6^{4x+3}\ -\ 15\ =\ 20\">\r<BR>\n" );
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document.write( "Add 15 to both sides and divide both sides by 5:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 6^{4x+3}\ =\ 7\">\r<BR>\n" );
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document.write( "Take the log of both sides -- but to which base?  Actually, in the final analysis, it doesn't matter.  The only thing that could possibly influence your decision would be if you have a calculator that can find the log to ANY valid base.  I don't know if the TI-84 will do that or not.  MS Excel will do it if you know how.  Assuming that you only have ln and log (base 10) available, pick one and proceed:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ln\left(6^{4x+3}\right)\ =\ \ln(7)\">\r<BR>\n" );
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document.write( "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( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (4x\,+\,3)\ln\left(6\right)\ =\ \ln(7)\">\r<BR>\n" );
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document.write( "Divide by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ln(6)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (4x\,+\,3)\ =\ \frac{\ln(7)}{\ln(6)}\">\r<BR>\n" );
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document.write( "Add -3 and divide by 4:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{\frac{\ln(7)}{\ln(6)}\ -\ 3}{4}\">\r<BR>\n" );
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document.write( "Is the exact answer -- use your calculator for a numeric approximation.\r<BR>\n" );
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document.write( "Now if you actually have the ability to take the log to any base, you can take the base 6 log, thus:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \log_6\left(6^{4x+3}\right)\ =\ \log_6(7)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (4x\,+\,3)\log_6\left(6\right)\ =\ \log_6(7)\">\r<BR>\n" );
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document.write( "But <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \log_6(6)\ =\ 1\">, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (4x\,+\,3)\ =\ \log_6(7)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{\log_6(7)\ -\ 3}{4}\">\r<BR>\n" );
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document.write( "A somewhat simpler calculation.\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" );
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