Question 107579
e^x=4sqrt(e^x)-3
e^x+3 = 4sqrt(e^x)
Square both sides to get:
e^2x + 6e^x + 9 = 16e^x
e^2x -10e^x + 9 = 0
(e^x-9)(e^x-1)=0
e^x=9 or e^x=1
x =ln9 or x=ln1
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Check these answers in e^x = 4sqrt(e^x)-3
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Checking x=ln(9)
e^(ln9)= 4sqrt(e^(ln9))-3
9 = 4*3-3
9 = 9
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Checking x = ln1
e^ln1 = 4sqrt(e^ln1)-3
e^0 = 4sqrt(1)-3
1 = 4-3
1 = 1
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Both solutions are good.
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Cheers,
Stan H.

Cheers,
Stan H.