Question

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. $3.7$

Answer 1

The correct option is C $2.9$

$x^z=y^2⟺{10}^{\left(0.48z\right)}={10}^{(2\times 0.70)}={10}^{1.40}$
$\Rightarrow 0.48z=1.40$
$\Rightarrow z=\frac{140}{48}=\frac{35}{12}=2.9$(approx.)