SOLUTION: 9ln(3x)=21

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Question 934574: 9ln(3x)=21
Found 2 solutions by jim_thompson5910, DrBeeee:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
9ln%283x%29=21


ln%283x%29=21%2F9


3x=e%5E%2821%2F9%29%5E%22%22


x=%281%2F3%29%2Ae%5E%2821%2F9%29%5E%22%22 Exact solution


x=3.4374195 Approximate solution (use a calculator)
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Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Given;
(1) 9ln(3x) = 21
Divide through by 9 and get
(2) ln(3x) = 21/9
Now take the inverse ln of each side to get
(3) 3x = invln(21/9) or
(4) 3x = 10.312258... and
(5) x = 3.437419...
We can express the answer exactly in terms of e, as follows;
Using (2), we have
(6) ln(3x) = 7/3 or
(7) 3x = invln(7/3) or
(8) 3x = e^(7/3) or
(9) x = (1/3)e^(7/3)