document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=112361>Question 112361</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 7^x-3/4=Square root of 6\r<BR>\n" );
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document.write( "PLEASE HELP! THANKS! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82047 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=82047\">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=7%5Ex-3%2F4+=+sqrt%286%29 ALIGN=MIDDLE  ALT=\"7%5Ex-3%2F4+=+sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F4 ALIGN=MIDDLE  ALT=\"-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the left side by adding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F4 ALIGN=MIDDLE  ALT=\"3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%5Ex+=+3%2F4+%2B+sqrt%286%29 ALIGN=MIDDLE  ALT=\"7%5Ex+=+3%2F4+%2B+sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The right side of this equation is just a number. We can find that number using a calculator.<BR>\n" );
document.write( "First, the fraction <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F4 ALIGN=MIDDLE  ALT=\"3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a decimal equivalent of 0.75. (You can find that by using<BR>\n" );
document.write( "a calculator to divide 4 (the denominator) into 3 (the numerator) and the calculator <BR>\n" );
document.write( "will give you the answer of 0.75<BR>\n" );
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document.write( "Then you can use a calculator to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%286%29 ALIGN=MIDDLE  ALT=\"sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The answer will be 2.449489743.<BR>\n" );
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document.write( "So the right side of the equation is 0.75 + 2.449489743 = 3.199489743<BR>\n" );
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document.write( "Therefore the equation is now:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%5Ex+=+3.199489743 ALIGN=MIDDLE  ALT=\"7%5Ex+=+3.199489743\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can solve this equation by taking the log to the base 10 of both sides to make the<BR>\n" );
document.write( "equation become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C7%5Ex%29+=+log%2810%2C3.199489743%29 ALIGN=MIDDLE  ALT=\"log%2810%2C7%5Ex%29+=+log%2810%2C3.199489743%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "On the right side you can use a calculator to find log(3.199489743). This log is 0.505080722.<BR>\n" );
document.write( "Substitute this value for the right side and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C7%5Ex%29+=+0.505080722 ALIGN=MIDDLE  ALT=\"log%2810%2C7%5Ex%29+=+0.505080722\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "When you take the log of a quantity raised to an exponent, you can bring the exponent out<BR>\n" );
document.write( "as a multiplier of the log.  This means that on the left side of the equation, the exponent<BR>\n" );
document.write( "x can be brought out as the multiplier of the log to give:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Alog%2810%2C7%29+=+0.505080722 ALIGN=MIDDLE  ALT=\"x%2Alog%2810%2C7%29+=+0.505080722\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Use a calculator to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C7%29 ALIGN=MIDDLE  ALT=\"log%2810%2C7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. If you do you will find that it is 0.84509804.<BR>\n" );
document.write( "Substitute this for the log and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2A0.84509804+=+0.505080722 ALIGN=MIDDLE  ALT=\"x%2A0.84509804+=+0.505080722\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve for x by dividing both sides of this equation to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+0.505080722%2F0.84509804+=+0.597659322 ALIGN=MIDDLE  ALT=\"x+=+0.505080722%2F0.84509804+=+0.597659322\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can check this answer by using a calculator to raise 7 to the exponent 0.597659322 <BR>\n" );
document.write( "If you do, you will find that the answer is 3.199489741. Take 3/4 (or 0.75) from this <BR>\n" );
document.write( "and you get that the left side of the original equation is 2.449489741. How does this left<BR>\n" );
document.write( "side compare with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%286%29 ALIGN=MIDDLE  ALT=\"sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is the right side of the original equation? <BR>\n" );
document.write( "As we found before, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%286%29+=+2.449489743 ALIGN=MIDDLE  ALT=\"sqrt%286%29+=+2.449489743\"   DISABLED_style= \"max-width:90%; height:auto;\" > ... close enough. So the answer of x = 0.597659322<BR>\n" );
document.write( "is correct.<BR>\n" );
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document.write( "Hope this helps you to understand the problem.<BR>\n" );
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document.write( " </SPAN>\n" );
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