Question

what common base can be used to rewrite each side of the equation $2^{x + 3}-3 = 5$?
○ 2
○ 3
○ 5
○ 8

Explanation:

Step1: Simplify the equation

First, solve the equation \(2^{x + 3}-3 = 5\) for the non - exponential part. Add 3 to both sides of the equation: \(2^{x+3}=5 + 3=8\).

Step2: Express 8 with base 2

We know that \(8 = 2\times2\times2=2^{3}\). The left - hand side of the equation \(2^{x + 3}\) has a base of 2, and we can express the right - hand side (8) with a base of 2 as \(2^{3}\). So the common base that can be used to rewrite each side of the equation is 2.

Answer:

A. 2