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Evaluate $\log_{\sqrt{5}} 125\sqrt{5}$.

Guest Dec 18, 2014

Best Answer 

 #1
avatar+17721 
+5

Let                                                     log√5125√5  =  x

Then write this into exponential notation:       √5x  =  125√5

Now, I want to write 125 with a base of √5:

   ---  first,  125  =  53

   ---  also,  (√5)2  =  5

   ---  so:    125  =   53  =  [ (√5)2 ]3  = (√5)6  

   ---  and:  125√5  =  (√5)6 ·√5  =  (√5)7

Thus:   √5x  =  (√5)7     --->  x = 7

geno3141  Dec 18, 2014
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1+0 Answers

 #1
avatar+17721 
+5
Best Answer

Let                                                     log√5125√5  =  x

Then write this into exponential notation:       √5x  =  125√5

Now, I want to write 125 with a base of √5:

   ---  first,  125  =  53

   ---  also,  (√5)2  =  5

   ---  so:    125  =   53  =  [ (√5)2 ]3  = (√5)6  

   ---  and:  125√5  =  (√5)6 ·√5  =  (√5)7

Thus:   √5x  =  (√5)7     --->  x = 7

geno3141  Dec 18, 2014

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