Describe and correct the error a student made when starting to solve the equation 8 ^ (x + 3) = 2 ^ (2x - 5) 8 ^ (x + 3) = 2 ^ (2x - 5) (2 ^ 3) ^ (x + 3) = 2 ^ (2x - 5) 2 ^ (3x + 3) = 2 ^ (2x - 5) Choose the correct answer below A. The student should have divided both sides by 2 ^ 2 to simplify the expression B. The student did not convert 8 to the correct power of 2 C. The student did not distribute 3 in * (2 ^ 3) ^ (x + 3) x + 3 D. The student should have expressed the initial rational exponent as the sum of two rational exponents ..

C. is the correct option

C. The student did not distribute 3 in * (2 ^ 3) ^ (x + 3) x + 3

and x = - 14

Step-by-step explanation:

8 ^ (x + 3) = 2 ^ (2x - 5)

Here is how the student solved the equation

8 ^ (x + 3) = 2 ^ (2x - 5)

8 ^ (x + 3) = 2 ^ (2x - 5)

(2 ^ 3) ^ (x + 3) = 2 ^ (2x - 5)

2 ^ (3x + 3) = 2 ^ (2x - 5) -----  This is where the student made the error.

The student did not distribute 3 in * (2 ^ 3) ^ (x + 3).

This is how to solve the equation

8 ^ (x + 3) = 2 ^ (2x - 5)

8 ^ (x + 3) = 2 ^ (2x - 5)

(2 ^ 3) ^ (x + 3) = 2 ^ (2x - 5)

Then, we will 3 distribute in  (2 ^ 3) ^ (x + 3), so that we get

2 ^ (3x +9) = 2 ^ (2x -5)

Since the bases on both sides of the equation are equal, we can equate the powers so that we get

(3x +9) = (2x -5)

Then we will collect like terms

3x - 2x = -5 -9

∴ x = -14

This solution could be better written in this format

x² + 3x + 7 = 0       [ax² + bx + c]

a = 1

b = 3

c = 7

quadratic formula:

    (+/- is this ±)

plug in the numbers into the variables

your answer is a

step by step solution :

step   1   :

1.1     4 = 22

(4)3 = (22)3 = 26

equation at the end of step   1   :

  ((23) • 26)2

step   2   :

equation at the end of step   2   :

  (23 • 26)2

step   3   :

final result :

  218

ya