explain the answerthe solution of equation4*4^4x=(256*4)^-1 is x=-1.5 and i think is wrong  

Expert Answers
justaguide eNotes educator| Certified Educator

We need the solution of the equation 4*4^4x = (256*4)^-1

4*4^4x = (256*4)^-1

=> 4*4^4x = 1/(256*4)

=> 4^4x = 1/256*4*4

=> 4^4x = 1/ 4^4*4^2

=> 4^4x = 1/4^(4 + 2)

=> 4^4x = 4^(-6)

As the base is the same we equate the exponent.

4x = -6

=> x = -6/4

=> x = -1.5

The answer x = -1.5 is right.

giorgiana1976 | Student

We notice that we must solve an exponential equation.

We also notice that the denominator of the fraction from the right side could be written as:

1024 = 256*4 = 4*16^2

We'll multiply both sides by 4:

1/16^2 = 4*4*16^2x

1/16^2 = 16*16^2x

We'll re-write the right side using the property of exponentials:

a^b*a^c = a^(b+c)

16*16^2x = 16^(1+2x)

We'll re-write the equation:

1/16^2 = 16^(1+2x)

16^(-2) = 16^(1+2x)

Since the bases are matching, we'll apply one to one property of exponentials:

2x+1=-2

2x=-2-1

2x=-3

The solution of the exponential equation 4*4^4x=(256*4)^-1 is x=-3/2 = -1.5 and it is the proper answer.