Mathematics: For what value or y does 125= (1/25) ^y-1

For what value or y does 125= (1/25) ^y-1 - id12512518371100, mcalepcrager

hubs14

05.02.2022

$125 = ({ \frac{1}{25} })^{y - 1} \\$

${5}^{3} = {(25})^{ ({ - 1})^{y - 1} }$

${5}^{3} = {25}^{ - (y - 1)}$

${5}^{3} = ({5})^{ ({2})^{ - (y - 1)} }$

${5}^{3} = {5}^{ - 2(y - 1)}$

The powers must equal to each other.

3 = - 2(y - 1)

Divided sides by -2

$\frac{3}{ - 2} = \frac{ - 2}{ - 2}(y - 1) \\$

$- \frac{ 3 }{2} = y - 1 \\$

Plus sides 1

$- \frac{3}{2} + 1 = y - 1 + 1 \\$

$- \frac{3}{2} + \frac{2}{2} = y \\$

$y = \frac{2 - 3}{2} \\$

$y = - \frac{1}{2} \\$

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And we're done....

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