Question

25. If 3x = 2^-xthen the value of x​

Answer 1

$3x=2^{-x}\\3x=e^{\ln 2^{-x}}\\3x=e^{-x \ln 2}\\\\\dfrac{1}{3x}=e^{x \ln 2}\\\\\dfrac{1}{3}=x e^{x\ln 2}\\\\\dfrac{\ln 2}{3}=x \ln 2e^{x\ln 2}\\\\x\ln 2=W\left(\dfrac{\ln 2}{3}\right)\\\\x=\dfrac{W\left(\dfrac{\ln 2}{3}\right)}{\ln 2}\approx0.28$