Question

solve $x$: $\frac{4^{x}+4^{x+2}}{2^{2x}} = 17$

Explanation:

Step1: Simplify numerator terms

Rewrite $4^x$ as $(2^2)^x=2^{2x}$, and $4^{x+2}=4^x \cdot 4^2=16 \cdot 4^x=16 \cdot 2^{2x}$.
Let $y=2^{2x}$, then numerator becomes $y + 16y = 17y$.

Step2: Substitute and simplify equation

Substitute into original equation: $\frac{17y}{y} = 17$ (where $y
eq 0$, which is always true since $2^{2x}>0$ for all real $x$).
This simplifies to $17=17$, which is an identity.

Answer:

All real numbers (any real value of $x$ is a solution)