SOLUTION: Hi I have searched for an eqjuation similar to the one I need to solve. Can you please help me? e^0.4x = 4^x-2

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Hi I have searched for an eqjuation similar to the one I need to solve. Can you please help me? e^0.4x = 4^x-2       Log On


   

Question 983082: Hi I have searched for an eqjuation similar to the one I need to solve. Can you please help me?
e^0.4x = 4^x-2
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
e^0.4x = 4^(x-2)
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Graph the left side and the right side on the same coordinate system.
Find the point of intersection.
graph%28400%2C400%2C-5%2C5%2C-5%2C5%2C2.71828%5E%280.4x%29%2C4%5E%28x-2%29%29
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Ans:: x = 2.8111....
Cheers,
Stan H.
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Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

e%5E%280.4x%29+=+4%5E%28x-2%29
e%5E%280.4x%29+=+%282%5E2%29%5E%28x-2%29
e%5E0.4x+=+2%5E%282x-4%29
log%28e%5E%280.4x%29%29+=+log%282%5E%282x-4%29%29
%280.4x%29log%28e%29+=+%282x-4%29log%282%29....since log%28e%29=1, we have

0.4x=%282x-4%29log%282%29
0.4x+=+2x%2Alog%282%29-4log%282%29
4log%282%29+=+2x%2Alog%282%29-+0.4x
4log%282%29+=+2x%28log%282%29-+0.2%29
2log%282%29+=+x%28log%282%29-+0.2%29
x=2log%282%29%2F%28log%282%29-+0.2%29
x=2.81112