Final answer:
The expression log₅2 + log₅x + log₅y simplifies to log₅(2xy) by using the property that the logarithm of a product is equal to the sum of the logarithms.
Step-by-step explanation:
The expression log₅2 + log₅x + log₅y can be simplified using the property of logarithms that states the logarithm of a product of two numbers is the sum of the logarithms of the two numbers. Applying this property, we can combine the individual logarithms into a single logarithm of the product of the variables. Therefore, the simplified form of the expression is log₅(2xy).
When you have the sum of logarithms, you can simplify it as the logarithm of the product. So, for the expression log52 + log5x + log5y, you can write it as log5(2xy).
For example, if x = 3 and y = 4, the expression would be log5(2 ⋅ 3 ⋅ 4) = log524 = 2.274. This means that the logarithm of the product of 2, x, and y in base 5 is 2.274.