(24^x)=9/(x * square root of 3) find the value of "x",

We are asked to solve ` 24^x=9/(xsqrt(3)) ` :

We can multiply both sides by x and simplify the right-hand side to get:

`x*24^x=3sqrt(3) `

I do not know of a simple algebraic way to solve this. We can use a graphing utility to graph the left side and the right side on the same coordinate axis and find the intersection. This yields `x~~.65275103 `

The graphs: