Simplify/Condense log base z of (xy^2)/64

Problem

(log_z)((x*y2)/64)

Solution

1. Apply the quotient rule for logarithms, which states that (log_b)(M/N)=(log_b)(M)−(log_b)(N)

(log_z)(x*y2)−(log_z)(64)

2. Apply the product rule for logarithms to the first term, which states that (log_b)(M*N)=(log_b)(M)+(log_b)(N)

(log_z)(x)+(log_z)(y2)−(log_z)(64)

3. Apply the power rule for logarithms to the middle term, which states that (log_b)(Mp)=p*(log_b)(M)

(log_z)(x)+2*(log_z)(y)−(log_z)(64)

4. Identify the constant in the final term. Since 64=2 or 4 or 8 it can be written in exponential form, but without a specific value for z the expression is fully expanded.

Final Answer

(log_z)((x*y2)/64)=(log_z)(x)+2*(log_z)(y)−(log_z)(64)

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