document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=85348>Question 85348</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having a hard time learning logarithm.<BR>\n" );
document.write( "Solve the equation. Give an exact solution.\r<BR>\n" );
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document.write( "4^(x+6) = 7 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #61576 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=61576\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E%28x%2B6%29+=+7 ALIGN=MIDDLE  ALT=\"4%5E%28x%2B6%29+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve for x<BR>\n" );
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document.write( "Take the log base 10 of both sides and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%284%5E%28x%2B6%29%29%29+=+log%28%287%29%29 ALIGN=MIDDLE  ALT=\"log%28%284%5E%28x%2B6%29%29%29+=+log%28%287%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "One of the rules of logarithms is that if you have the logarithm of a quantity that is<BR>\n" );
document.write( "raised to an exponent, it is equivalent to the exponent times the logarithm of just the<BR>\n" );
document.write( "quantity.<BR>\n" );
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document.write( "In this problem that translates to multiplying the exponent of (x + 6) times the logarithm of 4.<BR>\n" );
document.write( "This makes the equation become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B6%29%2Alog%28%284%29%29+=+log%28%287%29%29 ALIGN=MIDDLE  ALT=\"%28x%2B6%29%2Alog%28%284%29%29+=+log%28%287%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Divide both sides of the equation by log(4). When you do, the resulting equation is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B6%29+=+%28log%28%287%29%29%2Flog%28%284%29%29%29 ALIGN=MIDDLE  ALT=\"%28x%2B6%29+=+%28log%28%287%29%29%2Flog%28%284%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Next subtract 6 from both sides of the equation to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-6+%2B+%28log%28%287%29%29%2Flog%28%284%29%29%29 ALIGN=MIDDLE  ALT=\"x+=+-6+%2B+%28log%28%287%29%29%2Flog%28%284%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This is the basic answer. You can convert this to decimals by using a calculator  to determine<BR>\n" );
document.write( "the values of log(7) and log(4). When you do that you get that log(7) = 0.84509804 and<BR>\n" );
document.write( "log(4) = 0.602059991. Substituting these results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-+6+%2B%280.84509804%2F0.602059991%29 ALIGN=MIDDLE  ALT=\"x+=+-+6+%2B%280.84509804%2F0.602059991%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The division results in the equation becoming:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+-6+%2B+1.403677461+=+-4.596322539 ALIGN=MIDDLE  ALT=\"+x+=+-6+%2B+1.403677461+=+-4.596322539\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you understand the problem and how to use logarithms to solve it. </SPAN>\n" );
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