document.write( "Question 409554: Combine the following expression: log 12+(1/2) log 7 - log 2??? \r
\n" ); document.write( "\n" ); document.write( " Would the answe be log(84^(1/2) / 2)?? \n" ); document.write( "
Algebra.Com's Answer #288473 by jsmallt9(3758)\"\" \"About 
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\n" ); document.write( "\"log%28%2812%29%29%2B%281%2F2%29log%28%287%29%29+-+log%28%282%29%29\"
\n" ); document.write( "The properties that allow us to combine logarithms which have different arguments, \"log%28a%2C+%28p%29%29+%2B+log%28a%2C+%28q%29%29+=+log%28a%2C+p%2Aq%29%29\" and \"log%28a%2C+%28p%29%29+-+log%28a%2C+%28q%29%29+=+log%28a%2C+p%2Fq%29%29\", require that the coefficients of the logarithms be 1's. So we need to eliminate the (1/2) in front of the middle log. Fortunately there is another property, \"q%2Alog%28a%2C+%28p%29%29+=+log%28a%2C+%28p%5Eq%29%29\", which allows us to move a coefficient into the argument as the exponent. So we start by using this third property to move the 1/2:
\n" ); document.write( "\"log%28%2812%29%29%2Blog%28%287%5E%281%2F2%29%29%29+-+log%28%282%29%29\"
\n" ); document.write( "Since an exponent of 1/2 means square root, I am going to rewrite the argument as a square root:
\n" ); document.write( "\"log%28%2812%29%29%2Blog%28%28sqrt%287%29%29%29+-+log%28%282%29%29\"
\n" ); document.write( "Now we can start combining. The first two logs have a \"+\" between them so we will use the first property to combine them:
\n" ); document.write( "\"log%28%2812%2Asqrt%287%29%29%29+-+log%28%282%29%29\"
\n" ); document.write( "The remaining logs have a \"-\" between them so we will use the second property to combine them:
\n" ); document.write( "\"log%28%2812%2Asqrt%287%29%2F2%29%29\"
\n" ); document.write( "And finally the fraction will reduce:
\n" ); document.write( "\"log%28%286%2Asqrt%287%29%29%29\" \n" ); document.write( "
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