Subjects algebra

Logarithm Property 5C0724

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1. The problem asks which logarithm property is demonstrated by the equation $5^{109-5-10939} = 1098$. 2. Let's clarify the properties of logarithms: - Quotient Property: $\log_b \left(\frac{M}{N}\right) = \log_b M - \log_b N$ - Product Property: $\log_b (MN) = \log_b M + \log_b N$ - Power Property: $\log_b (M^p) = p \log_b M$ 3. The given equation is an exponential expression, not a logarithmic one, but the exponent is written as a subtraction: $109 - 5 - 10939$. 4. This subtraction in the exponent corresponds to the Quotient Property of logarithms, where subtraction inside a logarithm corresponds to division inside the argument. 5. Therefore, the equation demonstrates the Quotient Property of logarithms. Final answer: Quotient Property