Given that 10 0.48 = x, 10 0.70 = y and x z = y 2 , then the value of z is…
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Given that 10 0.48 = x, 10 0.70 = y and x z = y 2 , then the value of z is close to:
- A.
1.45
- B.
1.88
- C.
2.9
- D.
3.7
Attempted by 86 students.
Show answer & explanation
Correct answer: C
Answer: 2.9 (approx.)
Workings:
Given x = 10^{0.48} and y = 10^{0.70}, substitute into x^z = y^2.
(10^{0.48})^z = (10^{0.70})^2 ⇒ 10^{0.48·z} = 10^{1.40}.
Equate exponents: 0.48·z = 1.40.
Solve for z: z = 1.40 / 0.48 = 140/48 = 35/12 ≈ 2.9167 ≈ 2.9.
Key insight: express x and y as powers of 10, then compare exponents directly.