Solve the exponential equation by expressing each side as a power of the same base and then equating exponents.

The solution set is { }.
(Type an integer or a fraction. Simplify your answer. Use a comma to separate answers as needed.)

Question

Solve the exponential equation by expressing each side as a power of the same base and then equating exponents.

The solution set is { }.
(Type an integer or a fraction. Simplify your answer. Use a comma to separate answers as needed.)

UpStudy AI · Accepted Answer

1. Express $$16$$ and $$64$$ as powers of $$2$$:
   - $$16 = 2^4$$
   - $$64 = 2^6$$

2. Rewrite the equation $$16^x = 64$$ in terms of $$2$$:
   $$
   (2^4)^x = 2^6
   $$
   
3. Simplify the left side using the rule $$(a^b)^c = a^{bc}$$:
   $$
   2^{4x} = 2^6
   $$

4. Since the bases are the same, equate the exponents:
   $$
   4x = 6
   $$
   
5. Solve for $$ x $$:
   $$
   x = \frac{6}{4} = \frac{3}{2}
   $$

The solution set is $$\left\{ \frac{3}{2} \right\}$$.
The solution is $$ x = \frac{3}{2} $$.

Solve the exponential equation by expressing each side as a power of the same base and then equating exponents.

The solution set is { }.
(Type an integer or a fraction. Simplify your answer. Use a comma to separate answers as needed.)

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Solve the exponential equation by expressing each side as a power of the same base and then equating exponents. The solution set is { }. (Type an integer or a fraction. Simplify your answer. Use a comma to separate answers as needed.)

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Solve the exponential equation by expressing each side as a power of the same base and then equating exponents.

The solution set is { }.
(Type an integer or a fraction. Simplify your answer. Use a comma to separate answers as needed.)