Answer :
[tex]125 = ({ \frac{1}{25} })^{y - 1} \\ [/tex]
[tex] {5}^{3} = {(25})^{ ({ - 1})^{y - 1} } [/tex]
[tex] {5}^{3} = {25}^{ - (y - 1)} [/tex]
[tex] {5}^{3} = ({5})^{ ({2})^{ - (y - 1)} } [/tex]
[tex] {5}^{3} = {5}^{ - 2(y - 1)} [/tex]
The powers must equal to each other.
[tex]3 = - 2(y - 1)[/tex]
Divided sides by -2
[tex] \frac{3}{ - 2} = \frac{ - 2}{ - 2}(y - 1) \\ [/tex]
[tex] - \frac{ 3 }{2} = y - 1 \\ [/tex]
Plus sides 1
[tex] - \frac{3}{2} + 1 = y - 1 + 1 \\ [/tex]
[tex] - \frac{3}{2} + \frac{2}{2} = y \\ [/tex]
[tex]y = \frac{2 - 3}{2} \\ [/tex]
[tex]y = - \frac{1}{2} \\ [/tex]
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And we're done....
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