What is $\log _{15} 2^3$ rewritten using the power property?
A. $\log _{15} 5$
B. $\log _{15} 6$
C. $2 \log _{15} 3$
D. $3 \log _{15} 2$
Answer (2)
Apply the power property of logarithms: lo g b a c = c lo g b a .
Rewrite the expression using the power property: lo g 15 2 3 = 3 lo g 15 2 .
The rewritten expression is 3 lo g 15 2 .
The final answer is 3 lo g 15 2 .
Explanation
Understanding the Problem We are asked to rewrite the expression lo g 15 2 3 using the power property of logarithms.
Stating the Power Property The power property of logarithms states that lo g b a c = c lo g b a .
Applying the Property Applying the power property to the given expression, we have lo g 15 2 3 = 3 lo g 15 2 .
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, which can make calculations easier. Understanding the power property can help in analyzing exponential growth and decay, which are common in population studies and financial investments.
By applying the power property of logarithms, lo g 15 2 3 is rewritten as 3 lo g 15 2 . Therefore, the correct option is D. 3 lo g 15 2 .
;
