Solving the following exponential equation 43x=64 (1 point) Responses x=4 x=4 x=12 x is equal to 1 half x=34 x is equal to 3 fourths x=1

Answer 1

To solve the exponential equation \( 4^{3x} = 64 \), we start by expressing 64 as a power of 4.

Notice that: \[ 64 = 4^3 \]

This allows us to rewrite the equation: \[ 4^{3x} = 4^3 \]

Since the bases are the same, we can set the exponents equal to each other: \[ 3x = 3 \]

Now, divide both sides by 3: \[ x = 1 \]

Thus, the solution to the equation \( 4^{3x} = 64 \) is: \[ x = 1 \]

So, the correct response is \( x = 1 \).