Simplify/Condense 4 log of x+ log of y- log of z

Problem

4*(log_)(x)+(log_)(y)−(log_)(z)

Solution

1. Apply the power property of logarithms to the first term, which states n*(log_)(a)=(log_)(an)

(log_)(x4)+(log_)(y)−(log_)(z)

2. Apply the product property of logarithms to the first two terms, which states (log_)(a)+(log_)(b)=(log_)(a*b)

(log_)(x4*y)−(log_)(z)

3. Apply the quotient property of logarithms to the remaining terms, which states (log_)(a)−(log_)(b)=(log_)(a/b)

(log_)((x4*y)/z)

Final Answer

4*(log_)(x)+(log_)(y)−(log_)(z)=(log_)((x4*y)/z)

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