Question

4^x - 2^x+1 = 24 find x

Answer 1

Answer:

4^x - 4^(x-1) = 24 => 4^(x-1){4–1} = 24

=> 4^(x-1)×3 =24 => 4^(x-1)= 24/3

=>4^(x-1)= 8 => {(2^2)^(x-1)} = 2^3

=> 2^(2x-2) =2^3 ( since {a^m)^n} = a^mn)

=> 2x - 2 = 3 (since a^m=a^n=> m= n)

=> x = 5/2.

So. {(2x)^x}= {(2×5/2)}^(5/2)=5^(5/2) = 5^2×5^(1/2)

= 25√5