2^(x-1)+2^(2+x) =144 we can write
2^x / 2 + 2^2 *2^x = 144
2^x /2 + 4* 2^x = 144 multiply through by 2
2^x + 8*2^x = 288
9*2^x = 288 divide both sides by 9
2^x = 32 write 32 as 2^5
2^x = 2^5
So....x = 5
Solve for x :
2^(x - 1) + 2^(x + 2) = 144
Simplify and substitute y = 2^x.
2^(x - 1) + 2^(x + 2) = (9×2^x)/(2)
= (9 y)/2:
(9 y)/2 = 144
Multiply both sides by 2/9:
y = 32
Substitute back for y = 2^x:
2^x = 32
32 = 2^5:
2^x = 2^5
Equate exponents of 2 on both sides:
x = 5
2^(x-1)+2^(2+x)=144
\(\begin{array}{|rcll|} \hline 2^{x-1}+2^{2+x} &=& 144 \\ 2^{x-1}+2^{x+2} &=& 144 \quad & | \quad \cdot 2^3 \\ 2^{x-1}2^3+2^{x+2}2^3 &=& 144 *2^3 \\ 2^{x-1+3}+2^{x+2}*8 &=& 144 * 8 \\ 2^{x+2}+2^{x+2}*8 &=& 144 * 8 \\ 2^{x+2}*9 &=& 144 * 8 \quad & | \quad :9 \\ 2^{x+2} &=& \frac{144 * 8}{9} \\ 2^{x+2} &=& 16*8 \\ 2^{x+2} &=& 2^42^3 \\ 2^{x+2} &=& 2^{4+3} \\ 2^{x+2} &=& 2^{7} \\\\ x+2 &=& 7 \\ x&=& 7-2 \\ \mathbf{x} & \mathbf{=} & \mathbf{5} \\ \hline \end{array}\)