Question

Can you solve 2^x=e^(x+2)

Answer 1

`2^x=e^(x+2)\\ \\ ln(2^x)=ln(e^(x+2))\\ \\ xln(2)=(x+2)ln(e)\\ \\ xln(2)=x+2\\ \\ (x+2)/(x)=ln(2)\\ \\ (x)/(x)+(2)/(x)=ln(2)\\ \\ 1+(2)/(x)=ln(2)\\ \\ (2)/(x)=ln(2)-1\\ \\ \boxed{x=(2)/(ln(2)-1)}`

Answer 2

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)