(-9)^(1-2x)=1/81

Question

 Solve for x

Answer 1

Notice how 81 = (-9)². So 1/81 = (-9)^-2

 

(-9)^1-2x = 1/81

 

(-9)^1-2x = (-9)^-2

 

The bases on both sides match. Thus the exponents must match.

 

1-2x = -2

 

-2x = -3

 

x = 3/2

 

You can double check this answer by plugging it in.

 

(-9)^1-2x = (-9)^1-2(3/2) = (-9)^1-3 = (-9)^-2 = 1/(-9)² = 1/81