To solve the given equation `8^x=20` , we may take "ln" on both sides of the equation.

`ln(8^x)=ln(20)`

Apply natural logarithm property: `ln (x^n) = n*ln (x)` .

`xln(8)=ln(20)`

Divide both sides by `ln(8)` .

`(xln(8))/(ln(8))=(ln(20))/(ln(8))`

`x=(ln(20))/(ln(8)) or 1.441` (approximated value).

Checking: Plug-in `x=1.441` on `8^x=20` .

`8^1.441=?20`

`20.01 ~~20` ** TRUE**

Thus, the `x=(ln(20))/(ln(8))` is the real exact solution of the equation `8^x=20` .