Question

Solve for X
Pls give your working out as well x

Answer 1

`3^(x-2) = \left(\frac 13 \right)^(\sqrt x)\\ \\\implies 3^(x -2) = \left(3^(-1) \right)^(\sqrt x) \\\\\implies 3^(x-2) = 3^(-\sqrt x)\\\\\implies x -2 = -\sqrt x\\\\\implies (x-2)^2 = \left(-\sqrt x \right)^2\\\\\implies x^2 -4x +4 = x\\\\\implies x^2 -5x +4 =0\\\\\implies x^2 -4x-x+4=0\\\\\implies x(x-4) -(x-4)=0\\\\\implies (x-1)(x-4)=0\\\\\implies x = 1~~~~~~;[x = 4 ~ \text{Does not satisfy the original equation}]\\\\\text{Hence, x =1 is the solution.}`