If 2 x 1 3 1 x find x

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If 2 power x+1=3 power 1–x then find the value of x?

Answered by admin @


Answer:

The required value of x is given by :

x = \frac{\ln 1.5}{\ln 6}

Step-by-step explanation:

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}

Hence, The required value of x is given by :

x = \frac{\ln 1.5}{\ln 6}


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