document.write( "Question 253217: If f(x) = log2x, find f(16)
\n" ); document.write( "16=log 2x
\n" ); document.write( "2^16 =65,536
\n" ); document.write( "is this right \n" ); document.write( "

Algebra.Com's Answer #185447 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Not quite!
\n" ); document.write( "If $\"f%28x%29+=+Log%5B2%5D%28x%29\"$ find $\"f%2816%29\"$
\n" ); document.write( "Recall that the definition of the logarithm of a number is the \"power\" to which the \"base\" must be raised to equal that number. Or $\"Log%5Bb%5D%28x%29+=+y\"$ which can be expressed as: $\"b%5Ey+=+x\"$
\n" ); document.write( "In this problem, the 'base' is given as 2, and to find f(16) you must replace the x in the f(x) of the problem with 16, so now you have:
\n" ); document.write( " $\"f%2816%29+=+Log%5B2%5D%2816%29\"$
\n" ); document.write( "Let's rewrite the problem a bit replacing $\"f%2816%29\"$ wth $\"y\"$ :
\n" ); document.write( " $\"Log%5B2%5D%2816%29+=+y\"$ , then according to the above definition, we can write this as ( $\"Log%5Bb%5D%28x%29+=+y\"$ ---> $\"b%5Ey+=+x\"$ :
\n" ); document.write( " $\"2%5Ey+=+16\"$ Substitute $\"16+=+2%5E4\"$
\n" ); document.write( " $\"2%5Ey+=+2%5E4\"$ Now since the bases are equal, the exponents must be equal, so...
\n" ); document.write( " $\"y+=+4\"$ but $\"y+=+f%2816%29\"$ so...
\n" ); document.write( " $\"highlight%28f%2816%29+=+4%29\"$ \n" ); document.write( "

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