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Solve the exponential equation.
1/16=64^4x−3
To solve the exponential equation, we can rewrite the equation using the property of exponents that states:
a^(-n) = 1/(a^n)
So, we have:
1/16 = 64^(4x-3)
Rewriting 1/16 as (1/2)^4:
(1/2)^4 = 64^(4x-3)
Using the property of exponents that states:
(a^b)^c = a^(b*c)
we can rewrite the equation as:
1/2 = 64^(4x-3 * 4)
Simplifying the equation:
1/2 = 64^(16x - 12)
Rewriting 1/2 as 2^(-1):
2^(-1) = 64^(16x - 12)
Now, we can rewrite 64 as 2^6:
2^(-1) = (2^6)^(16x - 12)
Using the property of exponents stated earlier:
2^(-1) = 2^(6*(16x - 12))
Now, we can equate the exponents:
-1 = 6*(16x - 12)
Simplifying the equation:
-1 = 96x - 72
Adding 72 to both sides:
71 = 96x
Dividing both sides by 96:
x = 71/96