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

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