Question

Write as an exponential function and solve for the variable. Use * to indicate exponent.

5 = log2 Z.

a) Z = 25
b) Z = 32
c) Z = 2^5
d) Z = 2^-5

Answer 1

The equation 5 = log2 Z translates to Z = 2^5 in exponential form, and when calculated, Z equals 32.

Step-by-step explanation:

The student asked to write the equation 5 = log2 Z as an exponential function and solve for the variable Z. When working with logarithms, we can use the property that if a = logbc, then c = ba. Therefore, translating the given logarithmic equation to an exponential form we get Z = 25.

The value of Z is thus 2 raised to the power of 5. Using our knowledge of powers, we calculate that Z = 25 = 32. Hence, the correct answer is Z = 32, which corresponds to option b).