Question

27 exponent x divided by 3 is equal to one divided by 81.​

Answer 1

x = -1

Explanation:

27 exponent x =
`27^x`

Divided by 3 =
`(27^x)/(3)`

Is equal to :
`(1)/(81)`

Therefore,

`(27^x)/(3) = (1)/(81)`

Cross multiplying :

`27^x * 81 = 1 * 3`

`27^x = (3)/(81)`

`27^x = (1)/(27)`

`27^x = 27^(-1)`

`x = -1`
`[a^x = a^y => x = y]`

Answer 2

27 exponent x/3 = 1/81

we can say exponent as power also

(27 power x) × (3 power -1) = 81 power -1

(3 power 3x) × ( 3 power -1) = 3 power -4

IN MULTIPLICATION WHEN BASES ARE SAME THEN POWERS ARE ADDED

3 power 3x + (-1) = 3 power -4

IN AN EQUATION WHEN BASES ARE EQUAL POWERS ALSO EQUAL

3x +(-1) = -4

3x - 1 = -4

3x = -4 + 1

3x = -3

x = -3/3

x = -1