document.write( "Question 1197722: If p,q>0, log base p of q+ log base qof p=5/2 and pq=54√ 2, then find (p+q)/3 \n" ); document.write( "

Algebra.Com's Answer #831110 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "(1)

\n" ); document.write( "Given: $\"log%28p%2Cq%29%2Blog%28q%2Cp%29=5%2F2\"$

\n" ); document.write( " $\"log%28p%2Cq%29\"$ and $\"log%28q%2Cp%29\"$ are reciprocals: $\"log%28p%2Cq%29%2B1%2Flog%28p%2Cq%29=5%2F2\"$

\n" ); document.write( "Solve A+1/A = 5/2 to find the addends are 2 and 1/2: $\"log%28p%2Cq%29=2\"$

\n" ); document.write( " $\"log%28q%29%2Flog%28p%29=2\"$

\n" ); document.write( " $\"log%28q%29=2%2Alog%28p%29\"$

\n" ); document.write( " $\"log%28q%29=log%28p%5E2%29\"$

\n" ); document.write( " $\"q=p%5E2\"$

\n" ); document.write( "(2)

\n" ); document.write( " $\"pq=54sqrt%282%29\"$

\n" ); document.write( "Substitute $\"q=p%5E2\"$ and simplify:

\n" ); document.write( " $\"p%28p%5E2%29=54sqrt%282%29\"$

\n" ); document.write( " $\"p%5E3=54sqrt%282%29\"$

\n" ); document.write( " $\"p=3sqrt%282%29\"$

\n" ); document.write( " $\"q=p%5E2=18\"$

\n" ); document.write( "(3) Evaluate the given expression:

\n" ); document.write( " $\"%28p%2Bq%29%2F3=%283sqrt%282%29%2B18%29%2F3=sqrt%282%29%2B6\"$

\n" ); document.write( "ANSWER: $\"6%2Bsqrt%282%29\"$

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\n" ); document.write( "Added in response to question from student....

\n" ); document.write( "I arbitrarily chose to let $\"log%28p%2Cq%29=2\"$ . If I had chosen to let $\"log%28p%2Cq%29=1%2F2\"$ , the result would have been the same, with p and q switched.

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