If x = 101.4, y = 100.7, and xz = y3, then what is the value of z?

If x = 10^1.4, y = 10^0.7, and x^z = y³, then what is the value of z?

A 0.5

B 0.66

C 1.5

D 2

Correct Answer: Option C

x^z = y³ ⇒ (10^1.4)^z = (10^0.7)³
⇒ 10^1.4^z = 10^2.1⇒ 1.4z = 2.1
⇒ z = 2.1/1.4
⇒ z = 21/14
∴ z = 1.5