document.write( "Question 1192977: Express log3+log2 square root 2-3log 4 as a singular logarithm \n" ); document.write( "

Algebra.Com's Answer #824926 by greenestamps(13203) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "Note the concept of a \"singular logarithm\" is not defined....

\n" ); document.write( "To write the expression as a SINGLE logarithm, I will assume the expression is

\n" ); document.write( " $\"log%28%283%29%29%2Blog%28%282%2Asqrt%282%29%29%29-3%2Alog%28%284%29%29\"$

\n" ); document.write( "If that is the correct expression, then use your basic rules of logarithms:

\n" ); document.write( "(1) $\"log%28%28A%29%29%2Blog%28%28B%29%29=log%28%28AB%29%29\"$
\n" ); document.write( "(2) $\"log%28%28A%29%29-log%28%28B%29%29=log%28%28A%2FB%29%29\"$
\n" ); document.write( "(3) $\"n%2Alog%28%28A%29%29=log%28%28A%5En%29%29\"$

\n" ); document.write( "Using (1),

\n" ); document.write( "Using (3), $\"3%2Alog%28%284%29%29=log%28%284%5E3%29%29=log%28%2864%29%29\"$

\n" ); document.write( "Using (2),

\n" ); document.write( "ANSWER: $\"log%28%28%283%2Asqrt%282%29%29%2F32%29%29\"$

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\n" ); document.write( "NOTE...!

\n" ); document.write( "An answer in unsimplified form is more useful to a student who is just learning about logarithms:

\n" ); document.write( "ANSWER: $\"log%28%28%28%283%29%2A%282sqrt%282%29%29%29%2F4%5E3%29%29\"$

\n" ); document.write( "In that form you can still see all the parts of the given expression:
\n" ); document.write( "The (3) and 2*sqrt(2) are multiplied together; and
\n" ); document.write( "that product is divided by 4^3.

\n" ); document.write( " \n" ); document.write( "

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