Question

(4/3)^1-x = e^x (solve exponential equation)

Answer 1

we are given

`((4)/(3) )^(1-x)=e^x`

Since, we have to solve for x

so, firstly we will isolate x on any one side

we can take ln on both sides

`ln(((4)/(3) )^(1-x))=ln(e^x)`

now, we can simplify it

`(4-x)ln(((4)/(3) )=x`

now, we can move all x terms altogether

`4*ln((4)/(3))-xln((4)/(3))=x`

`xln((4)/(3))+x=4*ln((4)/(3))`

`x(ln((4)/(3))+1)=4ln((4)/(3))`

so, we get

`x=(4ln((4)/(3)))/((ln((4)/(3))+1))`...........Answer