Simplify/Condense 6 log base b of q- log base b of r

Problem

6*(log_b)(q)−(log_b)(r)

Solution

1. Apply the power property of logarithms to the first term, which states n*(log_b)(x)=(log_b)(xn)

6*(log_b)(q)=(log_b)(q6)

2. Apply the quotient property of logarithms, which states (log_b)(x)−(log_b)(y)=(log_b)(x/y)

(log_b)(q6)−(log_b)(r)=(log_b)((q6)/r)

Final Answer

6*(log_b)(q)−(log_b)(r)=(log_b)((q6)/r)

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