Question

(4^x2)^2 mulipled by 1/(4^5x)=64

Answer 1

I will rewrite my interpretation of the given equation as follows:

(4^x2)^2 mulipled by 1/(4^5x)=64
(4^(x²))² * 1/(4^5x = 64
Use the following laws of exponents:
x^a*x^b=x^a+b
x^a/x^b=x^a-b
(x^a)^b=x^ab
x^(1/a)=1/x^a
(4^(x²))² * 1/(4^5x = 64
(4^(x²))²/(4^5x = 4³
4^(2x²)/4^5x = 4³
4^(2x²-5x)=4³
Take logarithm to the base 4 on both sides to get:
2x²-5x=3
2x²-5x-3=0
Factor the quadratic to get
(2x+1)(x-3)=0
Can you take it from here?