document.write( "Question 627858: Evaluate the logarithmic expression. Do not round the expression until the final answer. When necessary, round to the nearest hundredth.\r
\n" ); document.write( "\n" ); document.write( "log[2]32 (1/5) \n" ); document.write( "

Algebra.Com's Answer #395257 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"log%282%2C+%2832%5E%281%2F5%29%29%29\"$
\n" ); document.write( "This expression is simple to evaluate if you understand what logarithms are and if you can figure out powers of 2. A base 2 logarithm, like yours, is an exponent that you would put one a 2. This particular logarithm is the exponent you would put on a 2 to get $\"32%5E%281%2F5%29\"$ as a result.

\n" ); document.write( "So what power of 2 does result in $\"32%5E%281%2F5%29\"$ ? The answer is easier than you think because 32 happens to be a power of 2! $\"32+=+2%5E5\"$ . Substituting this into your expression we get:
\n" ); document.write( " $\"log%282%2C+%28%282%5E5%29%5E%281%2F5%29%29%29\"$
\n" ); document.write( "Using our exponent rule for powers of a power (i.e. multiply the exponents) we get:
\n" ); document.write( " $\"log%282%2C+%282%29%29\"$
\n" ); document.write( "Now it is easy to see what power of 2 (the 2 in the base) results in a 2 (the 2 in the argument). It is 1! So:
\n" ); document.write( " $\"log%282%2C+%2832%5E%281%2F5%29%29%29+=+1\"$ \n" ); document.write( "

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