document.write( "Question 378530: log[64](32)=0\r
\n" ); document.write( "\n" ); document.write( "I keep coming up with no solution, but that isn't one of the answers on my pretest. Thanks! \n" ); document.write( "

Algebra.Com's Answer #269078 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
Where's the variable?? Without a variable there is no \"solution\" to be found. The equation is either true or not.

\n" ); document.write( "As for whether
\n" ); document.write( " $\"log%2864%2C+32%29+=+0\"$
\n" ); document.write( "is true or not, just rewrite it in exponential form:
\n" ); document.write( " $\"32+=+64%5E0\"$
\n" ); document.write( "Since any non-zero number to the zero power is 1 this simplifies to:
\n" ); document.write( " $\"32+=+1\"$
\n" ); document.write( "This is clearly a false statement.

\n" ); document.write( "P.S. We can find what $\"log%2864%2C+%2832%29%29\"$ equals without using calculators. Since both 64 and 32 are powers of 2 ( $\"64+=+2%5E6\"$ and $\"32+=+2%5E5\"$ , $\"log%2864%2C+%2832%29%29\"$ will simplify easily if we use the base conversion formula, $\"log%28a%2C+%28p%29%29+=+log%28b%2C+%28p%29%29%2Flog%28b%2C+%28a%29%29\"$ , to convert this base 64 logarithm into a base 2 logarithm:
\n" ); document.write( " $\"log%2864%2C+%2832%29%29+=+log%282%2C+%2832%29%29%2Flog%282%2C+%2864%29%29+=+5%2F6\"$ \n" ); document.write( "

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