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Given that 100.48 = x, 100.70 = y and xz = y2 then the value of z is close to = ?

Given that 100.48 = x, 100.70 = y and xz = y2 then the value of z is close to = ? Correct Answer 2.9

$$\eqalign{ & {x^z}{\text{ = }}{y^2}{\text{ }} \cr & \Leftrightarrow {\left( {{{10}^{0.48}}} \right)^z} = {\left( {{{10}^{0.70}}} \right)^2} \cr & \Leftrightarrow {10^{\left( {0.48z} \right)}} = {10^{\left( {2 \times 0.70} \right)}} = {10^{1.40}} \cr & \Leftrightarrow 0.48z = 1.40 \cr & \Leftrightarrow z = \frac{{140}}{{48}} = \frac{{35}}{{12}} \cr & \Leftrightarrow z = 2.9\left( {{\text{approx}}} \right) \cr} $$

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