Solve for x:
2 to x+1=x+2 to 3 or 2 to x+3= x+2 to x+5 (the proportions end up being the same in the end)
I keep getting to the part after you FOIL, and then I get stuck
To solve for x in the equation 2^(x+1) = (x+2)^3 or 2^(x+3) = (x+2)^(x+5, we need to simplify both equations and isolate x.
Let's solve the first equation, 2^(x+1) = (x+2)^3:
1. Distribute the exponent on the left side:
2 * 2^x = (x+2)^3
2. Expand the exponent on the right side:
2 * 2^x = (x+2)(x+2)(x+2)
3. FOIL the right side:
2 * 2^x = (x^2 + 4x + 4)(x+2)
4. Distribute and simplify further:
2 * 2^x = x^2(x+2) + 4x(x+2) + 4(x+2)
5. Expand and combine like terms:
2 * 2^x = x^3 + 2x^2 + 4x^2 + 8x + 4x + 8
6. Simplify the equation:
2^x+1 = x^3 + 6x^2 + 12x + 8
To continue solving, we need to use numerical or graphical methods since it is difficult to isolate x algebraically. There is no exact algebraic solution to this equation.