ABC26GN1963 · Surds and Indices
Subject: General Aptitude · Chapter: Surds and Indices · Exam: · Marks: · Difficulty:
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
Explanation
$$\begin{aligned} x^{z}=y^{2} & \Leftrightarrow\left(10^{0.48}\right)^{z}=\left(10^{0.70}\right)^{2} \\ & \Leftrightarrow 10^{(0.48 z)}=10^{(2 \times 0.70)}=10^{1.40} \\ & \Leftrightarrow 0.48 z=1.40 \\ & \Leftrightarrow z=\frac{140}{48}=\frac{35}{12}=2.9 \text { (approx.). } \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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