Find the value of x, if (2/3)^(-2) = (3/2)^(4) × (2/3)^(x)

Asked by palaktapadiya08.8spicertl | 3rd Jun, 2020, 02:17: PM

Expert Answer:

We need to find the value of x if (2/3)(-2) = (3/2)(4) × (2/3)(x)
This question can be solved using the laws of exponent as follows:
(2/3)-2 = (3/2)4 × (2/3)x
Using the property that a-m = 1/am, we get
(3/2)2 = (3/2)4 × (3/2)-x
Using the property, am x an = am+n, we get
(3/2)2 = (3/2)4-x
Now using the property, if am = an then m = n, we get
2 = 4 - x
x = 4 - 2
x = 2

Answered by Renu Varma | 3rd Jun, 2020, 04:52: PM