Can you solve 2^x=e^(x+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+2x ln(2) - x = 2x [ ln(2) - 1 ] = 2x = 2 / [ ln(2) - 1 ]x = 2 / -0.3069... = - 6.518... (rounded)
\(2^x=e^{x+2}\\ \\ ln(2^x)=ln(e^{x+2})\\ \\ xln(2)=(x+2)ln(e)\\ \\ xln(2)=x+2\\ \\ \frac{x+2}{x}=ln(2)\\ \\ \frac{x}{x}+\frac{2}{x}=ln(2)\\ \\ 1+\frac{2}{x}=ln(2)\\ \\ \frac{2}{x}=ln(2)-1\\ \\ \boxed{x=\frac{2}{ln(2)-1}}\)
