SOLUTION: Simplify the following expression and write it in simplified form. (Could you please show me step by step of how you did it) https://imgur.com/a/HnA2C

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Simplify the following expression and write it in simplified form. (Could you please show me step by step of how you did it) https://imgur.com/a/HnA2C      Log On


   

Question 1096787: Simplify the following expression and write it in simplified form.
(Could you please show me step by step of how you did it)
https://imgur.com/a/HnA2C
Found 2 solutions by Fombitz, Edwin McCravy:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Numerator:




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Denominator:



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So then,

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Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!




Use the fact that the sum of logs equals the log of the product
of what the logs are taken of:



Cancel what will cancel:

%22%22=%22%22

log%283%2C%283%2F9%29%29%2Flog%28%284%2F10%29%29%22%22=%22%22

log%283%2C%281%2F3%29%29%2Flog%28%284%2F10%29%29%22%22=%22%22

log%283%2C%283%5E%28-1%29%29%29%2Flog%28%284%2F10%29%29%22%22=%22%22 

%28%28-1%29log%283%2C%283%29%29%29%2F%28log%28%284%29%29-log%28%2810%29%29%29%22%22=%22%22

%28%28-1%29%281%29%29%2F%28log%28%284%29%29-1%29%22%22=%22%22

%28-1%29%2F%28log%28%284%29%29-1%29%22%22=%22%22

Multiply top and bottom by -1:

1%2F%28-log%28%284%29%29%2B1%29%22%22=%22%22

1%2F%281-log%28%284%29%29%29



Edwin