SOLUTION: write as a single logarithm=6log base 5 X + log base 5 Y

Question 392349: write as a single logarithm=6log base 5 X + log base 5 Y
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

These are not like terms so we cannot just add them. (If it had been then they would have been like terms and adding them would give us (just like 6q + q = 7q!)

But there is another way to combine two logarithms with a "+" between them into one. A property of logarithms, , allows us to combine two logarithms if all of the following are true:

There is a "+" between them.
The bases of the two logarithms are the same
The coefficients of the logarithms are 1's.

Your expression meets the first two requirements. But the first logarithm has a coefficient of 6. If we could eliminate that 6 then we would be in business. Fortunately there is another property of logarithms, , which allows us to "move" a coefficient into the argument of the logarithm as an exponent. Using this property on the first term we get:

Now we can use the first property to combine them into one:

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