What is x if 8^(4x-6)-1/64=0 ?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We have to find x given that 8^(4x-6)-1/64=0

8^(4x-6) - 1/64 = 0

=> 8^(4x-6) = 1/64

=> 8^(4x-6) = 8^-2

as the base is the same on both the sides we can equate the exponent.

=> 4x - 6 = -2

=> 4x = -2 + 6

=> 4x = 4

=> x  = 4/4

=> x = 1

Therefore x is equal to 1.

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

What is x if 8^(4x-6)-1/64=0.

We express 1/64 = 1/8^2  and rewrite the equation as below:

8^(4x-6)-1/8^2=0

8^(4x-6) = 1/8^2 = 8^(-2).

8^(4x-6) = 8^(-2).

Since the bases are same, we equate the exponents:

4x-6 = -2.

4x = -2+6

4x= 4.

4x/4 = 4/4 = 1.

x = 1.

Therefore x= 1.

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll write 64 = 8^2, so 1/64 = 1/8^2

We'll apply the rule of negative power:

1/8^2 = 8^-2

We'll re-write the equation:

8^(4x-6) = 8^-2

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

4x - 6 = -2

We'll isolate x to the left side:

4x = 6 - 2

4x = 4

We'll divide by 4:

x = 1

The only solution of the equation is x = 1.

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