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Can N be solved in the following equation using logs? I'm unable to do it. Thanks for help.

143.47=100*{[1.01]^N / [[1.01]^N - 1]}, solve for N.

Note: I know the answer but can't seem to solve it using logs.

 Oct 13, 2017
 #1
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143.47  =  100 * [ 1.01]^N / [ 1.01^N  - 1 ]      divide both sides by 100

 

1.4347  = 1.01^N / [ 1.01^N - 1]      note that we can write this as

 

 

1/ 1.4347  = 1 - 1/1.01^N     rearrange as

 

1/1.01^N  =  1 -   1/1.4347

 

1/1.01^N  = 4347 / 14347       and we can write this as

 

1.01^N  =   14347 / 4347        take the log of both sides

 

log 1.01^N  =  log [ 14347 / 4347 ]   and we can write

 

N* log 1.01  =  log [ 14347 / 4347]     divide both sides by log (1.01)

 

N  =  log [ 14347 / 4347]  / log (1.01)   ≈  120

 

 

cool cool cool

 Oct 13, 2017
 #2
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Terrific !! That is exactly the answer I have. Thank you very much.

 Oct 13, 2017

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