`7^(6x)=12` Solve the equation.

To solve the given equation `7^(6x)=12` , we may take "`ln` " on both sides of the equation.

`ln(7^(6x))=ln(12)`

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

`6x*ln(7)=ln(12)`

Divide both sides by `6ln(7)` .

`(6x*ln(7))/(6ln(7))=(ln(12))/(6ln(7))`

`x=(ln(12))/(6ln(7))`

`x=(ln(12))/(ln(117649)) ` or `0.213` (approximated value)

Checking: Plug-in `x=0.213` on `7^(6x)=12` .

`7^(6*0.213)=?12`

`7^(1.278)=?12`

`12.02~~12` TRUE

Thus, the `x=(ln(12))/(6ln(7))` is the real exact solution of the equation `7^(6x)=12` .

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