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

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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.

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