If z satisfies the equation 8^z = 256, then z is equal to __________.

A. log_16 8
B. log_2 8
C. 8/3
D. log_4 8

Question

If z satisfies the equation 8^z = 256, then z is equal to __________.

A. log_16 8
B. log_2 8
C. 8/3
D. log_4 8

Accepted Answer

z = 8/3 We need z such that 8 raised to z equals 256. Since 8 = 2^3 and 256 = 2^8, both sides can be expressed as powers of 2. Setting the exponents equal gives a simple linear equation in z. The answer 8/3 is a fraction just between 2 and 3, which makes sense since 8^2 = 64 and 8^3 = 512 straddle 256.

If z satisfies the equation 8^z = 256, then z is equal to __________. A. log_16 8 B. log_2 8 C. 8/3 D. log_4 8