document.write( "Question 604023: If log(2/5)=a , then define log(32) in terms of a \n" ); document.write( "
Algebra.Com's Answer #381082 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
When I looked at this problem, I found a solution by recognizing...
  • Since \"32+=+2%5E5\" it will be possible to express log(32) in terms of log(2):
    \n" ); document.write( "\"log%28%2832%29%29+=+log%28%282%5E5%29%29+=+5%2Alog%28%282%29%29\"
    \n" ); document.write( "using the property \"log%28a%2C+%28p%5Eq%29%29+=+q%2Alog%28a%2C+%28p%29%29\"
  • The property \"log%28a%2C+%28p%2Fq%29%29+=+log%28a%2C+%28p%29%29+-+log%28a%2C+%28q%29%29\" can be used to separate the 2 and the 5:
    \n" ); document.write( "\"log%28%282%2F5%29%29+=+a\"
    \n" ); document.write( "\"log%28%282%29%29+-+log%28%285%29%29+=+a\"
    \n" ); document.write( "From this we can get an expression for log(2):
    \n" ); document.write( "\"log%28%282%29%29+=+a+%2B+log%28%285%29%29\"

\n" ); document.write( "Substituting this expression into the log(32) expression we get:
\n" ); document.write( "\"log%28%2832%29%29+=+log%28%282%5E5%29%29+=+5%2A%28a+%2B+log%28%285%29%29%29\"
\n" ); document.write( "Distributing the 5 we get:
\n" ); document.write( "
\n" ); document.write( "which expresses log(32) in terms of a. \n" ); document.write( "
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