Write the equation in exponential form. \[ \log _{2} 32=5 \] The equation in exponential form is

Step 1 ：Write the equation in exponential form: \(\log _{2} 32=5\)

Step 2 ：The equation is in logarithmic form. To convert it to exponential form, we need to remember that the base of the logarithm becomes the base of the exponent, the result of the logarithm becomes the exponent, and the number the logarithm is equal to becomes the result of the exponentiation. In this case, the base of the logarithm is 2, the result of the logarithm is 5, and the number the logarithm is equal to is 32.

Step 3 ：Therefore, the equation in exponential form should be \(2^5 = 32\).

Step 4 ：Final Answer: The equation in exponential form is \(\boxed{2^5 = 32}\).