Question

2 ^ (x + 2) + 2 ^ (x - 1) + 2 ^ (x - 2) = 18

Answer 1

$\displaystyle \sf 2^{(x+2)}+2^{(x-1)}+2^{(x-2)} = 18 \\\\ 2^x\cdot 2^2+2^x\cdot 2^{-1}+2^x\cdot 2^{-2} = 18 \\\\ 4\cdot 2^x+\frac{2^x}{2}+\frac{2^x}{4}=18 \ \cdot (4)\\\\ 4\cdot 4\cdot 2^x+\frac{4\cdot 2^x}{2}+\frac{4\cdot 2^x}{4}=18\cdot 4 \\\\ 16\cdot 2^x+2\cdot 2^x+2^x= 72\\\\ 19\cdot 2^x=72 \\\\ 2^x=\frac{72}{19} \\\\ \ln (2)^x=\ln\left(\frac{72}{19}\right) \\\\ x\cdot \ln (2)=\ln\left(\frac{72}{19}\right) \\\\\\ x\ln (2) =\ln(72)-\ln(19)$

$\boxed{\ \sf x = \frac{\ln(72)-\ln(19) }{\ln (2)} \ }\checkmark$