You can put this solution on YOUR website! It would help greatly if you include the instructions with the problem. Tutors are not often willing to guess what a problem is and risk wasting their time providing a solution to what may even be the actual problem.
I am guessing that the problem is to rewrite
as a single logarithm. If so, then somehow we need to combine the three logarithms into one. For this we often use the properties of logarithms:
These properties can be used to combine two logarithms into one as long as the bases of the logarithms are the same and the coefficients of the logarithms are 1's.
And what if the coefficient is not a 1, like your first logarithm? Fortunatley there is another property of logarithms that comes to the rescue, , which allow us to move a coefficient into the argument as an exponent.
Now let's see how this works on your expression. As you might expect, we'll start with the two grouped logarithms at the end. They have the same base, 10, and their coefficients are 1's. So we can go right ahead and use the first property (because of the "+" between the logarithms) to combine them:
or
Now we use the third property to move the coefficients into the arguments as exponents:
Since an exponent of 1/2 means square root, the argument of the first logarithm becomes:
Now we'll use the second property (because of the "-" in between the logs) to combine the remaining logarithms. (Note: we could not have used this property before we had changed the coefficients to 1's.)
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