What is x if 2^(9x-15)-1/64=0 ?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

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We need to find x if 2^(9x-15) - 1/64 = 0

2^(9x-15) - 1/64 = 0

move 1/64 to the other side

=>2^(9x-15) = 1/64

express 1/64 in terms of powers of 2

=> 2^(9x-15) = 2^(-6)

as the base is equal equate the exponent

9x - 15 = -6

=> 9x = 9

=> x = 1

The solution of 2^(9x-15) - 1/64 = 0 is x = 1

Top Answer

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll move 1/64 to the right side and we'll write it as a power of 2:

1/64 = 1/2^6

We'll apply the negative power rule:

1/2^6 = 2^-6

We'll re-write the equation:

2^(9x-15) = 2^-6

Since the bases are matching, we'll use the one to one property of exponentials and we'll get:

9x - 15 = -6

We'll divide by 3:

3x - 5 = -2

We'll move the number alone to the right side:

3x = 5 - 2

3x = 3

x = 1

The real solution of the equation is x = 1.

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