SOLUTION: 9e^x=28 what is the solution set in terms of natural logarithms? what is the decimal approximation of the solution? round two decimal places as needed

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Question 1006800: 9e^x=28
what is the solution set in terms of natural logarithms?
what is the decimal approximation of the solution? round two decimal places as needed
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
We will use these log rules


Rule 1) Ln%28x%5Ey%29=y%2ALn%28x%29


Rule 2) Ln%28e%29=1


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9e%5Ex=28


%289e%5Ex%29%2F9=28%2F9 Divide both sides by 9


e%5Ex=28%2F9


Ln%28e%5Ex%29=Ln%2828%2F9%29 Apply natural logs to both sides


x%2ALn%28e%29=Ln%2828%2F9%29 Use rule 1 (see above)


x%2A1=Ln%2828%2F9%29 Use rule 2 (see above).


x=Ln%2828%2F9%29 This is the exact answer in terms of natural logs.


x=1.13497993283899 Use a calculator to compute Ln(28/9)


x=1.13 Round to two decimal places