Question

(4/16^(y_2)×(1/4)^y=64(^_2y_1)
Find the value of y?

Answer 1

`4 * {16}^( - (y - 2) ) * {4}^( - y) = ({4})^{ ({3})^( (- 2y - 1)) } \\`

`4 * ({4})^{ ({2})^((y - 2)) } * {4}^( - y) = {4}^( - 6y - 3)`

`4 * {4}^((2y - 4)) * {4}^( - y) = {4}^( - 6y - 3)`

`{4}^(1 + 2y - 4 - y) = {4}^( - 6y - 3) \\`

`{4}^(y - 3) = {4}^( - 6y - 3)`

Thus ;

`y - 3 = - 6y - 3`

Plus sides 3

`y - 3 + 3 = - 6y - 3 + 3`

`y = - 6y`

Plus sides 6y

`y + 6y = - 6y + 6y`

`7y = 0`

Divided sides by 7

`(7)/(7)y = (0)/(7) \\`

`y = 0`

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Check :

`0 - 3 = - 6(0) - 3`

`- 3 = 0 - 3`

`- 3 = - 3`

Thus this is the correct value.

Done.....♥️♥️♥️♥️♥️