Simplify $\frac{4^{x+2}-2^{2x+1}}{8^x(4^{1-x})}$ and express it in the form $a(2^{x-b})$ where \

Question

Simplify $\frac{4^{x+2}-2^{2x+1}}{8^x(4^{1-x})}$ and express it in the form $a(2^{x-b})$ where $a$ and $b$ are integers. [3] Hence, solve for $x$ if $\frac{4^{x+2}-2^{2x+1}}{8^x(4^{1-x})} = 15$. [2]

Accepted Answer

(a) $14(2^{x-2})$, so $a=14$, $b=2$. (b) $x=2.10$ (3 s.f.).

Indices - Laws of Indices

Indices - Laws of Indices

Video Solution:

Default solution