Simplify/Condense

Problem

3*(log_3)(x)+4*(log_3)(y)−4*(log_3)(z)

Solution

1. Apply the Power Property of logarithms, which states n*(log_b)(a)=(log_b)(an) to each term in the expression.

(log_3)(x3)+(log_3)(y4)−(log_3)(z4)

2. Apply the Product Property of logarithms, which states (log_b)(a)+(log_b)(c)=(log_b)(a*c) to the first two terms.

(log_3)(x3*y4)−(log_3)(z4)

3. Apply the Quotient Property of logarithms, which states (log_b)(a)−(log_b)(c)=(log_b)(a/c) to combine the remaining terms into a single logarithm.

(log_3)((x3*y4)/(z4))

Final Answer

3*(log_3)(x)+4*(log_3)(y)−4*(log_3)(z)=(log_3)((x3*y4)/(z4))

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