Solve 16x x = 0.25

Solve 16x ${}^x$ = 0.25

Answer Details

First, let's begin by rewriting the given equation:

16^x = 0.25

To solve for x, we need to express both sides of the equation as powers of the same base. Notice that:

16 is 2⁴ (because 16 is 2 multiplied by itself 4 times)

0.25 can be rewritten as a fraction, which equals 1/4. 1/4 is the same as 2^-2 (because 4 is 2 squared, so the reciprocal 1/4 is the same as 2^-2)

Rewriting the equation in terms of powers of 2, we have:

(2⁴)^x = 2^-2

Using the property of exponents that says (a^m)ⁿ = a^m*n, we can rewrite the left side as:

2^4x = 2^-2

Since the bases are now the same (both are base 2), we can set the exponents equal to each other:

4x = -2

Now, solve for x:

Divide both sides by 4:

x = -2/4

Simplifying the fraction gives:

x = -1/2

Since the provided options do not include -1/2, it seems there might be a typo or misunderstanding in the options provided. If the options are indeed as listed, then none of them is correct for this equation as solved above. Please recheck the options or consult with your instructor for further clarification.