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VashaNatasha [74]
4 years ago
14

 Can you solve 2^x=e^(x+2)

Mathematics
2 answers:
mina [271]4 years ago
8 0
<u>Answer:</u> Yes, I can.


Although you haven't asked for the solution, here it is anyway:

2^x = e^(x+2)

x ln(2) = x+2

x ln(2) - x = 2

x [ ln(2) - 1 ] = 2

x = 2 / [ ln(2) - 1 ]

x = 2 / -0.3069... =<u> - 6.518</u>... (rounded) 

serg [7]4 years ago
7 0
2^x=e^{x+2}\\&#10;\\&#10;ln(2^x)=ln(e^{x+2})\\&#10;\\&#10;xln(2)=(x+2)ln(e)\\&#10;\\&#10;xln(2)=x+2\\&#10;\\&#10;\frac{x+2}{x}=ln(2)\\&#10;\\&#10;\frac{x}{x}+\frac{2}{x}=ln(2)\\&#10;\\&#10;1+\frac{2}{x}=ln(2)\\&#10;\\&#10;\frac{2}{x}=ln(2)-1\\&#10;\\&#10;\boxed{x=\frac{2}{ln(2)-1}}
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