Question

If 2^x-2.3^2x-6=36, Find the value of X.

Answer 1

Answer:

x = 4

Step-by-step explanation:

If 2^x-2.3^2x-6=36, Find the value of X.

2⁽ˣ⁻²⁾ * 3⁽²ˣ⁻⁶) = 36

first factorize 36

36 = 2 * 18

18 = 2 * 9

9 =  3 * 3

=> 36 = 2 * 2 * 3 * 3

=> 36 = 2² * 3²

2⁽ˣ⁻²⁾ * 3⁽²ˣ⁻⁶)  = 2² * 3²

as 2 & 3 are co-prime numbers

so we can compare their powers individually

2⁽ˣ⁻²⁾ = 2²

=> x -2 = 2

=> x = 4

or

3⁽²ˣ⁻⁶) = 3²

=> 2x - 6 = 2

=> 2x = 8

=> x = 4

The value of X = 4  if  2⁽ˣ⁻²⁾ * 3⁽²ˣ⁻⁶) = 36