Question

8. If 2 to the power of x+1 = 3 to the power of 1-x then find the value of x.​

Answer 1

Answer:

Answer:

The required value of x is given by :

x = \frac{\ln 1.5}{\ln 6}x=ln6ln1.5

Step-by-step explanation:

\begin{gathered}2^{x+1}=3^{1-x}\\\\\text{Taking natural log on both the sides}\\\\\implies (x+1)\ln 2=(1-x)\ln 3\\\\\implies x\ln 2+ \ln 2=\ln 3-x\ln 3\\\\\implies x\ln 2+x\ln 3=\ln 3-\ln 2\\\\\implies x(\ln 2 +\ln 3) = \ln 3-\ln 2\\\\\implies x\ln 6=\ln 1.5\\\\\implies x = \frac{\ln 1.5}{\ln 6}\end{gathered}2x+1=31−xTaking natural log on both the sides⟹(x+1)ln2=(1−x)ln3⟹xln2+ln2=ln3−xln3⟹xln2+xln3=ln3−ln2⟹x(ln2+ln3)=ln3−ln2⟹xln6=ln1.5⟹x=ln6ln1.5

Hence, The required value of x is given by :

x = \frac{\ln 1.5}{\ln 6}x=ln6ln1.5