Verified answer

You are going to need to understand a few log properties in order to solve this problem

1. a log n = log n^a....meaning 6 log 8 = log8^6 (just a basic example)....the log of a power is equal to the power times the log of the base.

2. log(base b) x + log(base b) x = log (base b)(x*y)...the sum of logs = the log of products

3. log(base b) x - log(base b) x = log (base b)(x/y)...the difference of logs is the log of quotients

Pat1.

step 1:

we use the first log property to get rid of the coefficients in the equation

log (base 5) x^2 + log(base 5)y^(1/2) - log(base 5) z^4 = log 5 ((x^2) (y^(1/2)) / (z^4)

step 2:

We use the second property in order to add the logarithms with same base

log (base 5) (x^2*y^(1/2))- log(base 5) z^4 = log (base 5) ((x^2) (y^(1/2)) / (z^4)

step 3:

We use the third property to subtract logarithms with same base

log (base 5) ((x^2*(y^(1/2)))/(z^4)= log (base 5) ((x^2)* (y^(1/2)))/ (z^4)

once completing step 3 you can now see the the equation is true...both sides of the equals sign are identical

part 2.

we begin by using the log property that states that the log of a power is equal to the power times the log of the base. Applying this property to the equation allows us to "get rid" of the coefficients in the equation so that addition and subtraction of the logs might be made simpler. We then use the log property that states that the log of a product is equal to the sum of the logs of the factors. By using this property we are able to add the logarithms in the equation that contain the same base. Finally we use the log property that states that the log of a quotient is equal to the difference between the logs of the numerator and denominator. By using this property we are able to subtract the logarithms in the equation that contain that same base. After applying these 3 log properties in solving and simplifying the equation, we are able to reach the conclusion that the equation is true

I hope this helps :)