document.write( "Question 200367: If a^(1/3)+b^(1/3)+c^(1/3)=0, then show that log[(a+b+c)/3]=1/3[loga+logb+logc] \n" ); document.write( "

Algebra.Com's Answer #150659 by orca(409) $\"\"$ $\"About$

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$\"a%5E%281%2F3%29%2Bb%5E%281%2F3%29%2Bc%5E%281%2F3%29=0\"$
\n" ); document.write( " $\"a%5E%281%2F3%29%2Bb%5E%281%2F3%29=-c%5E%281%2F3%29\"$
\n" ); document.write( " $\"%28a%5E%281%2F3%29%2Bb%5E%281%2F3%29%29%5E3=%28-c%5E%281%2F3%29%29%5E3\"$ cube both sides
\n" ); document.write( " $\"a%2B3a%5E%282%2F3%29b%5E%281%2F3%29%2B3a%5E%281%2F3%29b%5E%282%2F3%29%2Bb=-c\"$
\n" ); document.write( " $\"a%2Bb%2B3a%5E%281%2F3%29b%5E%281%2F3%29%28a%5E%281%2F3%29%2Bb%5E%281%2F3%29%29=-c\"$
\n" ); document.write( " $\"a%2Bb%2Bc%2B3a%5E%281%2F3%29b%5E%281%2F3%29%28a%5E%281%2F3%29%2Bb%5E%281%2F3%29%29=0\"$
\n" ); document.write( "Noting that $\"a%5E%281%2F3%29%2Bb%5E%281%2F3%29=-c%5E%281%2F3%29\"$ , we have
\n" ); document.write( " $\"a%2Bb%2Bc%2B3a%5E%281%2F3%29b%5E%281%2F3%29%28-c%5E%281%2F3%29%29=0\"$
\n" ); document.write( " $\"a%2Bb%2Bc=3a%5E%281%2F3%29b%5E%281%2F3%29c%5E%281%2F3%29\"$
\n" ); document.write( " $\"%28a%2Bb%2Bc%29%2F3=a%5E%281%2F3%29b%5E%281%2F3%29c%5E%281%2F3%29\"$
\n" ); document.write( "So
\n" ); document.write( "log[(a+b+c)/3]=1/3[loga+logb+logc] \n" ); document.write( "

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