Solve the logarithmic equation explaining the properties used log 6 (3x+14)-log 6 (5) = log 6 (2x)

First, we have to use the quotient property of the logarithms:

 log 6 [(3x+14)/5] = log 6 (2x)

Now, we'll have to use the one to one property, that means that:

 log 6 [(3x+14)/5] = log 6 (2x) if and only if (3x+14)/5=2x

After cross multiplying, we'll get:

3x+14=10x

We'll move the terms to one side:

10x-3x=14

7x=14

x=14/7

x=2

If we'll check the solution into equation, we'll get:

log 6 [(3*2+14)/5] = log 6 (2*2)

log 6 [(20)/5] = log 6 (4)

log 6 (4) = log 6 (4)