document.write( "Question 116270: Bear with me I'm not sure how to enter certain symbols:( Sorry.)
\n" ); document.write( "Expand as much as possible and evaluate:\r
\n" ); document.write( "\n" ); document.write( "log3(base) then radicand symbol (index is 4) and x^5 y^4/81 is inside the
\n" ); document.write( "radicand symbol.\r
\n" ); document.write( "\n" ); document.write( "I noticed the two equations inside the radicand symbol were divided so I
\n" ); document.write( "know this means I have to write it as subtraction.\r
\n" ); document.write( "\n" ); document.write( "log3(x^5y^4)^1/4-log3 (81)1/4
\n" ); document.write( "log3 (x^5/4 y^4/4) - 1/4 log3 (81)?
\n" ); document.write( "5/4 log3 X + 4/4 log3 Y - 9/4?\r
\n" ); document.write( "\n" ); document.write( "Please help our study group was coming up with 3 different answers and I'm not
\n" ); document.write( "sure any of us were sure what to do.:) \n" ); document.write( "
Algebra.Com's Answer #84565 by bucky(2189)\"\" \"About 
You can put this solution on YOUR website!
Given:
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\n" ); document.write( "\"log%283%2Croot%284%2C%28x%5E5%2Ay%5E4%29%2F81%29%29\"
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\n" ); document.write( "Your work was:
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\n" ); document.write( " <=== ok
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\n" ); document.write( "\"log%283%2C+%28x%5E%285%2F4%29%29%2A%28+y%5E%284%2F4%29%29%29+-+%281%2F4%29%2Alog%283%2C81%29\"<=== ok
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\n" ); document.write( "\"%285%2F4%29%2A+log%283%2Cx%29+%2B+%284%2F4%29%2A+log%283%2Cy%29+-+9%2F4\" <=== mistake in last term
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\n" ); document.write( "You have a mistake in evaluating \"%28-1%2F4%29+%2Alog%283%2C81%29\". Replace 81 with \"3%5E4%29\" and the term
\n" ); document.write( "becomes:
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\n" ); document.write( "\"%28-1%2F4%29+%2Alog%283%2C3%5E4%29\"
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\n" ); document.write( "Bring the exponent 4 out as a multiplier and the result is:
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\n" ); document.write( "\"%28-1%2F4%29%2A4+%2Alog%283%2C3%29\"
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\n" ); document.write( "But \"log%283%2C3%29+=+1\"
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\n" ); document.write( "so this reduces to:
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\n" ); document.write( "\"%28-1%2F4%29+%2A+4+%2A+1+=+-1\"
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\n" ); document.write( "So in your last equation replace - 9/4 with -1 and you have:
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\n" ); document.write( "\n" ); document.write( "\"%285%2F4%29%2A+log%283%2Cx%29+%2B+%284%2F4%29%2A+log%283%2Cy%29+-+1\"
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\n" ); document.write( "and in the second term note that \"4%2F4+=+1\" so the expression reduces to:
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\n" ); document.write( "\"%285%2F4%29%2A+log%283%2Cx%29+%2B+log%283%2Cy%29+-+1\"
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\n" ); document.write( "That should be enough to convince your teacher that you know what you are doing. I'm not sure
\n" ); document.write( "what else could be productively done on this problem. If you feel that it needs more work,
\n" ); document.write( "post it again with the above change to your work and see if some other tutor has another idea
\n" ); document.write( "about how to go further.
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\n" ); document.write( "Hope this helps you and the study group. Check my work and ensure that I haven't made a \"late night\"
\n" ); document.write( "error.
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