Simplify/Condense log base 6 of y-2 log base 6 of z

Problem

(log_6)(y)−2*(log_6)(z)

Solution

1. Identify the expression as a difference of two logarithmic terms with the same base.

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

(log_6)(y)−(log_6)(z2)

3. Apply the quotient property of logarithms, which states (log_b)(M)−(log_b)(N)=(log_b)(M/N) to condense the expression into a single logarithm.

(log_6)(y/(z2))

Final Answer

(log_6)(y)−2*(log_6)(z)=(log_6)(y/(z2))

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