Question

Need help please thank you

Answer 1

D. x = -7/3

Explanation:

A graphical solution is often easier when the problem is written in the form f(x) = 0. That way, the x-intercept(s) of the function f(x) will be the solution.

F(x) = 0

The desired form can be found by subtracting 16 from both sides of the equation:

`\left((1)/(64)\right)^(-x-3)=16\qquad\text{given}\\\\\left((1)/(64)\right)^(-x-3)-16=0\quad\Longrightarrow\quad f(x)=\left((1)/(64)\right)^(-x-3)-16`

A graph is attached, showing x=-7/3 is the solution.

Algebraic solution

Using powers of 4, the equation can be rewritten ...

`\left((1)/(4^3)\right)^(-x-3)=4^2\qquad\text{given}\\\\4^(3(x+3))=4^2\\\\3(x+3)=2\qquad\text{equating exponents, or taking base-4 logs}\\\\x=(2)/(3)-3=\boxed{-(7)/(3)}\qquad\text{divide by 3, subtract 3}`