Answer :
we are given
[tex] (\frac{4}{3} )^{1-x}=e^x [/tex]
Since, we have to solve for x
so, firstly we will isolate x on any one side
we can take ln on both sides
[tex] ln((\frac{4}{3} )^{1-x})=ln(e^x) [/tex]
now, we can simplify it
[tex] (4-x)ln((\frac{4}{3} )=x [/tex]
now, we can move all x terms altogether
[tex] 4*ln(\frac{4}{3})-xln(\frac{4}{3})=x [/tex]
[tex] xln(\frac{4}{3})+x=4*ln(\frac{4}{3}) [/tex]
[tex] x(ln(\frac{4}{3})+1)=4ln(\frac{4}{3}) [/tex]
so, we get
[tex] x=\frac{4ln(\frac{4}{3})}{(ln(\frac{4}{3})+1)} [/tex]...........Answer