Write the equation in its equivalent exponential form. Then solve for \( x \). \( \log _{4}(x-5)=3 \) \( \log _{4}(x-5)=3 \) in its equivalent exponential form is \( \square \). (Do not simplify.)

To convert the logarithmic equation \( \log_{4}(x-5) = 3 \) into its equivalent exponential form, we follow the definition of logarithms. The equation states that \( 4 \) raised to the power of \( 3 \) equals \( x - 5 \). Thus, the equivalent exponential form is: \[ 4^3 = x - 5 \] Now, we can solve for \( x \): 1. Calculate \( 4^3 \): \[ 4^3 = 64 \] 2. Set the equation: \[ 64 = x - 5 \] 3. Add \( 5 \) to both sides to isolate \( x \): \[ x = 64 + 5 \] 4. Therefore: \[ x = 69 \] So, the equivalent exponential form is \( 4^3 = x - 5 \) and the solution for \( x \) is \( 69 \).