SOLUTION: Combine the following expression: log 12+(1/2) log 7 - log 2??? Would the answe be log(84^(1/2) / 2)??

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Question 409554: Combine the following expression: log 12+(1/2) log 7 - log 2???
Would the answe be log(84^(1/2) / 2)??

Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!
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The properties that allow us to combine logarithms which have different arguments, and , 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, , 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:

Since an exponent of 1/2 means square root, I am going to rewrite the argument as a square root:

Now we can start combining. The first two logs have a "+" between them so we will use the first property to combine them:

The remaining logs have a "-" between them so we will use the second property to combine them:

And finally the fraction will reduce:

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