Evaluate the logarithm. log ⁡ 36 216 \log _ { 36 } 216 lo g 36 216 A) 3 2 \frac { 3 } { 2 } 2 3 B) 3C) 2 3 \frac { 2 } { 3 } 3 2 D) 6E) log ⁡ 36 216 \log _ { 36 } 216 lo g 36 216 is undefined.

Question

Evaluate the logarithm.   log ⁡ 36 216 \log _ { 36 } 216 lo g 36 ​ 216 A)    3 2 \frac { 3 } { 2 } 2 3 ​ B) 3C)    2 3 \frac { 2 } { 3 } 3 2 ​ D) 6E)    log ⁡ 36 216 \log _ { 36 } 216 lo g 36 ​ 216   is undefined.

Franky freemen · Accepted Answer

Final Answer : A, Explanation :   log ⁡ 36 216 \log_{36} 216 lo g 36 ​ 216   can be simplified by recognizing that   36 = 6 2 36 = 6^2 36 = 6 2   and   216 = 6 3 216 = 6^3 216 = 6 3  . Thus,   log ⁡ 6 2 6 3 = 3 2 \log_{6^2} 6^3 = \frac{3}{2} lo g 6 2 ​ 6 3 = 2 3 ​  , because   6 2 × 3 2 = 6 3 6^{2 	imes \frac{3}{2}} = 6^3 6 2 × 2 3 ​ = 6 3  .

Evaluate the logarithm. $log _ { 36 } 216$

A) $32\frac { 3 } { 2 }$
B) 3
C) $23\frac { 2 } { 3 }$
D) 6
E) $log _ { 36 } 216$ is undefined.

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Evaluate the logarithm. log⁡36216\log _ { 36 } 216log36​216 A) 32\frac { 3 } { 2 }23​ B) 3C) 23\frac { 2 } { 3 }32​ D) 6E) log⁡36216\log _ { 36 } 216log36​216 is undefined.

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Learning Objectives

Learning Objectives

Related questions

Evaluate the logarithm. $log _ { 36 } 216$

A) $32\frac { 3 } { 2 }$
B) 3
C) $23\frac { 2 } { 3 }$
D) 6
E) $log _ { 36 } 216$ is undefined.