By applying the natural logarithm to both sides, we will see that the solution for the exponential equation is y = -0.5
Solving the exponential equation:
Here we want to solve:
125 = (1/25)^(y - 1)
To do it, we need to remove the variable from the exponent, to do that we must apply the natural logarithm to both sides, remember that:
ln(a^x) = x*ln(a).
Then we will get:
ln(125) = ln( (1/25)^(y - 1))
ln(125) = ln(1/25)*(y - 1)
Now we can solve this for y:
y = ln(125)/ln(1/25) + 1 = -0.5
Then the solution is y = -0.5
If you want to learn more about exponential equations, you can read:
https://brainly.com/question/11464095
