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`81^(x-1) = 1/3^(2x)`

Reduce the bases in terms of prime numbers - ie 3

`(3^4)^(x-1) = (3^-1)^(2x)` In terms of the rules of exponents, when a number is divided this equates to a (-) when the base is transferred to the top of the equation.

`3^(4x-4) = 3^(-2x)`  Remember to multiply the exponents when they are bracketed like this

As the bases are the same now you can form an equation with the powers, thus:

`4x-4 = -2x`

`4x + 2x = 4`

`6x= 4`

`x= 4/6`  Then simplify and check your answer by substituting the x values and then the left hand side will equal the right hand side

x= 2/3

 

 

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