The inverse of y = 5 log x is:, x = 5 log y, x = y log 5, y = x 1 log 5, x = 5 1 log y

Given, y = 5 log x y = x log 5 ∴ b log a = a log b y 1 log 5 = x Replacing x → y and y → x x 1 log 5 = y

The inverse of y = 5 log x is:

Question: Answered & Verified by Expert

The inverse of

y = 5^{\log x}

is:

MathematicsFunctionsJEE MainJEE Main 2021 (17 Mar Shift 1)

Options:

Solution:

2353 Upvotes Verified Answer

The correct answer is:

y = x^{\frac{1}{\log 5}}

Given, $y = 5^{\log x}$

$y = x^{\log 5} (∴ b^{\log a} = a^{\log b})$

$y^{\frac{1}{\log 5}} = x$

Replacing $x \to y$ and $y \to x$

$x^{\frac{1}{\log 5}} = y$

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