SOLUTION: I have a work sheet w/ some natural logs that I need help with. e^x * e^(3x) = 4 e^9 = (e^x)^3 (1/e^9) Thank you so much!

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Question 71077: I have a work sheet w/ some natural logs that I need help with.
e^x * e^(3x) = 4
e^9 = (e^x)^3 (1/e^9)
Thank you so much!
Found 2 solutions by Earlsdon, jim_thompson5910:
Answer by Earlsdon(6294)   (Show Source): You can put this solution on YOUR website!
1) Solve for x:
Take the natural log of both sides.
Apply the product rule for logarithms to the left side.
But
Simplify.
Divide both sides by 4.
Evaluate using your calculator or log tables.
Approximately.
2) Solve for x:
Multiply both sides by
Simplify both sides.
Take the natural log of both sides.

Divide both sides by 3.
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Start with given expression
The left side can be written as since
Take natural log of both sides, this undoes the natural base e
Solve for x by dividing both sides by 4
Approximately


Do the same thing to the next problem
Start with given expression
The right side can be rewritten as since (in other words )
Multiply both side by e^9
Take natural log of both sides, this undoes the natural base e
Solve for x by dividing both sides by 3

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