Question 18448: I am trying to use logarithms to find the fifth root of 37.
The procedure I used gives me the wrong answer.What have I done wrong?
To get the fifth root of 37 I did the following:
1)Designated the fifth root of 37 as 37^1/5
2)Looked up 3.7 in the common log table to get .5682
3)Divided .5682 by 5 to get .1137
4)Found the antilog of .1137 to be about 1.30
But this is the wrong answer. I know this because this problem was worked out somewhere else and the correct answer is 2.0589. To get this answer, the following steps were made:
antilog(log(37)/5=
antilog(3.6109/5)=
antilog(.7221)=
2.0589
In terms of the latter correct solution, I do not understand how the 3.6109 number is derived. Also, I assume that the antilog I found is incorrect if the antilog times .7221 is the answer of 2.0589.
I would really appreciate knowing the nature of my errors and how this problem was solved correctly. I imagine I need a more basic explanation concerning the necessary steps and procedures about how to solve this problem in terms of the corrent explanation.
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! I am trying to use logarithms to find the fifth root of 37.
The procedure I used gives me the wrong answer.What have I done wrong?
To get the fifth root of 37 I did the following:
1)Designated the fifth root of 37 as 37^1/5......OK
2)Looked up 3.7 in the common log table to get .5682.....OK
3)Divided .5682 by 5 to get .1137...................OK
PLEASE NOTE THAT YOU DID NOT TAKE THE FULL VALUE OF LOG 37..LOG HAS 2 PARTS..CHARACTERSTIC & MANTISSA. YOU FOUND MANTISSA > IT IS OK > BUT CHARACTERSTIC IS 1 FOR 37 WHICH YOU DID NOT PUT ..SO THE LOG IS ACTUALLY 1.5682..I HOPE YOU KNOW THIS [LOG TABLES GIVE LOGS FOR VALUES UPTO 10 ONLY.YOU FOUND LOG FOR 3.7 NOT 37 AS IS REQUIRED.TO TAKE THIS INTO ACCOUNT WE WRITE LOG37=LOG(10*3.7)=LOG10+LOG3.7=1+0.5682=1.5682].SO DIVIDING 1.5682 WITH 5 WE GET 0.3136....ANTILOG OF WHICH IS 2.05892 ..THIS IS THE CORRECT ANSWER.
4)Found the antilog of .1137 to be about 1.30
But this is the wrong answer. I know this because this problem was worked out somewhere else and the correct answer is 2.0589. To get this answer, the following steps were made:
antilog(log(37)/5=
antilog(3.6109/5)=NO ...NOT... REPEAT NOT CORRECT
antilog(.7221)= MISTAKE
2.0589....MISTAKE ...THIS IS ALL WRONG .WHAT YOU HAVE DONE IS MORE CORRECT AND YOU ALMOST GOT IT BUT FOR THE MITAKE ON CHARACTERSTIC...IF YOU HAVE ANY FURTHER BASIC DOUBT COME BACK AND I WILL CLARIFY..ACTUALLY THIS IS SIMPLER...MORE DIFFICULT WOULD HAVE BEEN TO DO 5TH.ROOT FOR 0.37 ...TRY THAT AND YOU WILL MASTER LOGS THEN..GOOD LUCK
In terms of the latter correct solution, I do not understand how the 3.6109 number is derived. Also, I assume that the antilog I found is incorrect if the antilog times .7221 is the answer of 2.0589.
I would really appreciate knowing the nature of my errors and how this problem was solved correctly. I imagine I need a more basic explanation concerning the necessary steps and procedures about how to solve this problem in terms of the corrent explanation.
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