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Question

Solve the exponential equation.

1/16=64^4x−3

Answer 1

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