Simplify the expression $\log _ { 5 } 150$.
A) $2 + \log _ { 5 } 6$
B) $30 \log _ { 5 } 2$
C) 6
D) $2 \log _ { 5 } 6$
E) The expression cannot be simplified.

Question

Quizplus · Accepted Answer

The expression $\log _ { 5 } 150$ can be simplified by breaking down 150 into its prime factors, which are 2, 3, and 5^2. Thus, $\log _ { 5 } 150 = \log _ { 5 } (2 \cdot 3 \cdot 5^2) = \log _ { 5 } 2 + \log _ { 5 } 3 + \log _ { 5 } 5^2 = \log _ { 5 } 2 + \log _ { 5 } 3 + 2 = 2 + \log _ { 5 } (2 \cdot 3) = 2 + \log _ { 5 } 6$.

Simplify the Expression log⁡5150\log _ { 5 } 150log5​150 A) 2+log⁡562 + \log _ { 5 } 62+log5​6

Simplify the Expression $\log _ { 5 } 150$
A) $2 + \log _ { 5 } 6$