ems99
ems99
26-05-2014
Mathematics
Answered
Can you solve 2^x=e^(x+2)
Answer :
AL2006
AL2006
26-05-2014
Answer:
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... =
- 6.518
... (rounded)
Answer Link
Ryan2
Ryan2
26-05-2014
[tex]2^x=e^{x+2}\\ \\ ln(2^x)=ln(e^{x+2})\\ \\ xln(2)=(x+2)ln(e)\\ \\ xln(2)=x+2\\ \\ \frac{x+2}{x}=ln(2)\\ \\ \frac{x}{x}+\frac{2}{x}=ln(2)\\ \\ 1+\frac{2}{x}=ln(2)\\ \\ \frac{2}{x}=ln(2)-1\\ \\ \boxed{x=\frac{2}{ln(2)-1}}[/tex]
Answer Link
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