Simplify/Condense ( log of a)/( log of b)

Problem

(log_)(a)/(log_)(b)

Solution

1. Identify the expression as a quotient of two logarithms with the same implicit base (usually base 10 or base e.

2. Apply the change of base formula, which states that for any positive bases b and k and any positive number a

(log_k)(a)/(log_k)(b)=(log_b)(a)

3. Rewrite the expression in its condensed form using b as the new base.

Final Answer

(log_)(a)/(log_)(b)=(log_b)(a)

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