JEE PYQ: Functions Question 2
Question 2 - 2021 (17 Mar Shift 1)
The inverse of $y = 5^{\log x}$ is:
(1) $x = (1/y)^{\log 5}$
(2) $x = y^{\frac{1}{\log 5}}$
(3) $x = 5^{\log y}$
(4) $x = 5^{\frac{1}{\log y}}$
Type: MCQ
Show Answer
Answer: (3) $x = 5^{\log y}$
Solution
$y = 5^{\log x}$
$y = x^{\log 5}$
$y^{\frac{1}{\log 5}} = x$
Replacing $x \to y$ and $y \to x$: $x = 5^{\log y}$