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Simplify 6^log(base36)9

Simplify 
 
6^log(36)9

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Michael F. | Mathematics TutorMathematics Tutor
4.7 4.7 (6 lesson ratings) (6)
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6(log369)=6(log69/log636)=6(log69)/2=√9=3, since 6log69=9
Jason S. | My goal is the success of my students. Knowledge-Patience-HonestyMy goal is the success of my students. K...
4.9 4.9 (115 lesson ratings) (115)
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6^(log369)

Use "change of base":

log36 9 = (log6 9)/(log6 36)

Since log6 36 = 2,

6^(log369) = 6^((log6 9)/2) = (6^(log6 9))1/2


(6^(log6 9))1/2

Since 6^(log6 9) = 9

(9)1/2 = sqrt(9) = 3


Answer:
3

Comments

Where did the square root come or to the 1/2 power?