Question

Show that 2^[x+1]-2^[x-1]= 15 can be written as 2[2^x]-1/2[2^x]= 15

Answer 1

$~~~~~~2^{x+1} - 2^{x-1} = 15\\\\\implies 2^x \cdot 2^1 - 2^x \cdot 2^{-1}=15~~~~~~~~~~~~~~~~~~;[a^m \times a^n = a^{m+n}]\\\\\implies 2 \left(2^x\right) - \dfrac 12 \left(2^x \right) = 15~~~~~~~~~~~~~~~~~~~~;\left[a^{-n} = \dfrac 1{a^n},~~~a\neq 0 \right]\\\\\text{Showed.}$

Answer 2

Answer:

Step-by-step explanation:

2^[x+1]-2^[x-1]

=2^x×2-[2^x]÷2

=2[2^x]-1/2[2^x]

so 2^[x+1]-2^[x-1]= 15 can be written as 2[2^x]-1/2[2^x]= 15 !