Solve 81^(x-1)=(1/3)^(2x) for x.

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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**

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

3^(4x-4) = 3^(-2x)

4x-4 = -2x

6x = 4

Thus x = 2/3

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