Question

For what values of y does 125=(1/25)^y-1

Answer 1

`125 = (1)/(125) {}^(y - 1) \\ 125 = ( {5}^( - 2) ) {}^(y - 1) \\ \\ {5}^(3) = {5}^(2 - 2y) \\ 3 = 2 - 2y \\ - 0.5 = y`

Answer 2

The answer is
`y=-0.5`

Explanation:

In order to determine the "y" value, we have to change the way of we see the equation.

In these cases, when the variable is in the exponent and it is possible to make two exponents in each side of the equation, we have to equal bases and then we have to make other equation between the exponents of both sides.

So,

`125=((1)/(25))^y^-^1\\(5)^3=(5^-^2)^y^-^1\\(5)^3=(5)^-^2^*^y^+^2\\`

Then, we have to make an equation between the exponents of both sides:

`3=-2*y+2\\2*y=2-3\\2*y=-1\\y=(-1)/(2)=-0.5\\ y=-0.5`

Finally, the value of "y" is -0.5