Question

if 2^x+1=3^1-x then find the value of x

Answer 1

Take log on both sides
(x+1)log2=(1-x)log3

Alternatively, (x+1)/(1-x)=log3/log2
Take componendo and dividendo on both sides:

2/2x=(log3+log2)/(log3-log2)

Take reciprocal,

X=(log3-log2)/(log3+log2) 

Since the values for Log3=0.4771 and Log2=0.3010

x= 0.2263

Verification: 
LHS=2^(1.2263)=2.3397
RHS=3^(0.7737)=2.3397

Hence proved!
hope it helps