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