To solve the given equation `7^(3x)=18` , we may take "ln" on both sides of the equation.

`ln(7^(3x))=ln(18)`

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

`3xln(7)=ln(18)`

Divide both sides by `3ln(7)` .

`(3xln(7))/(3ln(7))=(ln(18))/(3ln(7))`

`x=(ln(18))/(3ln(7))`

`x= (ln(18))/(ln(343))or 0.495` (approximated value).

Checking: Plug-in `x=0.495` on `7^(3x)=18` .

`7^(3*0.495)=?18`

`7^(1.485)=?18`

`17.99 ~~18` **TRUE**

Thus, the `x=(ln(18))/(3ln(7))` is the** real exact solution** of the equation `7^(3x)=18` .

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