Respuesta :
Answer:
Log_k(x * z^3 / y^2)
Step-by-step explanation:
To simplify the expression Log_k(x) - 2Log_k(y) + 3Log_k(z) as a single logarithm of a single argument, we need to apply the properties of logarithms.
1. Use the power rule of logarithms: Log_a(b^n) = n * Log_a(b).
2. Apply the power rule to each term in the expression:
Log_k(x) - 2Log_k(y) + 3Log_k(z)
= Log_k(x) - Log_k(y^2) + Log_k(z^3)
3. Use the product rule of logarithms: Log_a(b) + Log_a(c) = Log_a(bc).
4. Combine the terms using the product rule:
= Log_k(x * z^3 / y^2)
Therefore, the simplified expression of Log_k(x) - 2Log_k(y) + 3Log_k(z) as a single logarithm of a single argument is Log_k(x * z^3 / y^2).
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