Question

HELP ASAP PLEASE

What is the solution to the equation 16 ^2x -3 . 4^-2x = 4^2?
A. x=4
B. x=-A
C. x=2
D. x=1

Answer 1

The correct answer is,

A. x = 4

Explanation:

We have the equation,

`16^(2x)-3(4^(-2x))=4^2`

Solving this, we get,

`16^(2x-3)(4^(-2x))=4^2\\(4^2)^(2x-3)(4^(-2x))=4^2\\(4^(4x-6))(4^(-2x))=4^2\\4^(4x-2x-6)=4^2\\4^(2x-6)=4^2\\4^(2x)4^(-6)=4^2\\4^(2x)=4^24^6\\4^(2x)=4^(2+6)\\4^(2x)=4^8\\`

comparing coefficients,

we get,

2x = 8,

x = 8/2

x = 4

Answer 2

x=256/4093 aka 0.06254580991

B

meaning that x is less than answer choices A,C and D meaning ur answer is B