If \(10^{0.48}=x\), \(10^{0.70}=y\) and \(x^z=y^2\), then the value of \(z\) is closest to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 2.9
When both sides are written as powers of the same base, the exponents must be equal. Here the base is 10, and \(\left(10^m\right)^n=10^{mn}\).
\(x^z=\left(10^{0.48}\right)^z=10^{0.48z}\)
\(y^2=\left(10^{0.70}\right)^2=10^{1.40}\)
\(0.48z=1.40\)
\(z\displaystyle=\frac{1.40}{0.48}=\frac{35}{12}\approx2.92\), which is closest to 2.9