Final answer:
The given logarithmic expression, 2logₓ(y) + 7logₓ(z), can be simplified by applying the properties of logarithms. By using the property that the logarithm of a product is the sum of the logarithms, we can combine the logarithms into one. The simplified form is logₓ(y²z⁷).
Step-by-step explanation:
The given expression is 2logₓ(y) + 7logₓ(z). We can apply the property of logarithm that states the logarithm of a product of two numbers is the sum of the logarithms of the two numbers. Therefore, we can rewrite the expression as 2logₓ(y) + 7logₓ(z) = logₓ(y²) + logₓ(z⁷).
Using the property of addition of logarithms, we can combine these two logarithms into one: logₓ(y²z⁷).
So, the simplified form of the expression is logₓ(y²z⁷).