document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=244998>Question 244998</A>: <I><SPAN STYLE=\"word-break: break-all;\"> given log(base a)x=4, log(base a)y=3, and log(base a)z=2 for constants x, y,z. find the value of the logarithm.\r<BR>\n" );
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document.write( "log(base a)((5th root of y^3 times x^6 times z^4)/(5th root of z^6 times x^2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #853599 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=853599\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find the value of the logarithmic expression, we use the properties of logarithms to expand and simplify the expression into terms we already know.\r<BR>\n" );
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document.write( "### Given:\r<BR>\n" );
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document.write( "1. <BR>\n" );
document.write( "2. <BR>\n" );
document.write( "3. \r<BR>\n" );
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document.write( "### Expression to find:\r<BR>\n" );
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document.write( "---\r<BR>\n" );
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document.write( "### Step 1: Simplify the expression inside the logarithm\r<BR>\n" );
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document.write( "Using the laws of exponents ( and ):\r<BR>\n" );
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document.write( "* For : <BR>\n" );
document.write( "* For : <BR>\n" );
document.write( "* For : \r<BR>\n" );
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document.write( "The expression simplifies to:\r<BR>\n" );
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document.write( "---\r<BR>\n" );
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document.write( "### Step 2: Use Logarithm Rules to expand\r<BR>\n" );
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document.write( "Applying the product rule () and the power rule ():\r<BR>\n" );
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document.write( "---\r<BR>\n" );
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document.write( "### Step 3: Substitute the given values\r<BR>\n" );
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document.write( "Substitute , , and :\r<BR>\n" );
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document.write( "Combine the fractions:\r<BR>\n" );
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document.write( "Convert to decimal form:\r<BR>\n" );
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document.write( "**Final Answer:**<BR>\n" );
document.write( "The value of the logarithm is **23.4**. </SPAN>\n" );
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