Questions: Solve 4^(2x) = sqrt[5](64) exactly. A. x=3/10 B. x=5/6 C. x=3/5 D. x=-3/10

Solution Steps

The given equation is \(4^{2x} = \sqrt[5]{64}\). We need to express both sides with the same base if possible.

The right side, \(\sqrt[5]{64}\), can be rewritten as \(64^{1/5}\). Since \(64 = 4^3\), we have:

\[ \sqrt[5]{64} = (4^3)^{1/5} = 4^{3/5} \]

Now that both sides have the same base, we equate the exponents:

\[ 2x = \frac{3}{5} \]

To solve for \(x\), divide both sides by 2:

\[ x = \frac{3}{5} \times \frac{1}{2} = \frac{3}{10} \]

Final Answer