SOLUTION: Express as a single logarithm,and, if possible, simplify Logb5x+7(logbx � logby)

Question 269655: Express as a single logarithm,and, if possible, simplify
Logb5x+7(logbx � logby)
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Taking an expression of multiple logarithms as a single logarithm requires that we know the properties of logarithms:

The first two are used to combine two logarithms into one. The first one is use when there is a "+" between the two logs. The second one is used when there is a "-" between the two logs. The first two properties require that the two logarithms have coefficients of 1 in front of them. The third property is used to move other coefficients into the argument of the logarithm. Let's see how this works on your expression:

We'll start by combining the two logarithms in the parentheses using the second property:

Before we combine the last two logarithms we need to have coefficients of 1. So that 7 needs to go. This is where the thrid property comes in handy:

Now we can combine the last two logarithms (with the first property):

which simplifies to

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