Given that 10 0.48 = x, 10 0.70 = y and x z = y 2 , then the value of z is close to: Options: A . &nbsp1.45 B . &nbsp1.88 C . &nbsp2.9 D . &nbsp3.7

Given that 100.48 = x, 100.70 = y and xz =&nb

Question

Given that 10^0.48 = x, 10^0.70 = y and x^z = y², then the value of z is close to:

Options:

A . 1.45

B . 1.88

C . 2.9

D . 3.7

Answer: Option C

x^z = y² \(\Leftrightarrow \) 10^(0.48z) = 10^{(2 x 0.70)} = 10^1.40

0.48z = 1.40

z = \(\frac{140}{48}\) = \(\frac{35}{12}\) = 2.9 (approx.)

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