Question

$find the value of x if 2^{4} * 2^{5} =( 2^{5}) ^{x}$

Answer 1

2^4 * 2^5 = (2^5) ^x

⇒ 2^ (4+5) = 2^5x  [ ∵ a^m * a^n = a^ (m+n);  (a^m) ^n = a^ (m*n) ]

⇒2^9 = 2^5x
⇒9= 5x  [∵if a^m = a^n ⇔ m=n]
∴9/5= x
x= 9/5