What is $\log _6 e^f$ rewritten using the power property?
A. $e \log _6 f$
B. $f \log _6 e$
C. $\log _6(e \cdot f)$
D. $\log _c(e+f)$
Answer (2)
Apply the power property of logarithms: lo g b a c = c lo g b a .
Rewrite the expression lo g 6 e f using the power property.
The rewritten expression is f lo g 6 e .
The final answer is f lo g 6 e .
Explanation
Understanding the Problem We are given the expression lo g 6 e f . We need to rewrite it using the power property of logarithms. The power property of logarithms states that lo g b a c = c lo g b a .
Applying the Power Property The power property of logarithms states that lo g b a c = c lo g b a . In our case, b = 6 , a = e , and c = f . Therefore, lo g 6 e f = f lo g 6 e .
Final Answer The expression lo g 6 e f rewritten using the power property is f lo g 6 e .
Examples
Logarithms are used in many scientific fields, such as physics, chemistry, and engineering. For example, the Richter scale, which measures the magnitude of earthquakes, is a logarithmic scale. The power property of logarithms is useful in simplifying logarithmic expressions and solving logarithmic equations. For instance, if you are analyzing the intensity of sound and need to simplify an expression involving logarithms, you can use the power property to make the calculations easier.
The expression lo g 6 e f can be rewritten using the power property of logarithms as f lo g 6 e . The correct answer is option B: f lo g 6 e . This showcases how logarithmic functions can simplify the handling of exponential terms.
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