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JEE Main 202117 MarchMorning Shift
Exam
JEE Main
Year
2021
Date
17 March
Shift
Morning Shift
Subject
Mathematics
Chapter
Functions

JEE Main 2021 · 17 March · Morning Shift · Mathematics · Functions

The inverse of y = 5 ^ x is:

The inverse of y=5log⁡xy = {5}^{\log x} is:

Options

  1. Ax=5log⁡yx = {5}^{\log y}
  2. Bx=ylog⁡5x = {y}^{\log 5}
  3. Cy=x1log⁡5y = x\dfrac{1}{\log 5}
  4. Dx=51log⁡yx = 5\dfrac{1}{\log y}

Correct answer

C. y=x1log⁡5y = x\dfrac{1}{\log 5}

Step-by-step solution

Given, y=5log⁡xy = {5}^{\log x}

y=xlog⁡5(∴bloga=alogb)y = {x}^{\log 5}\left(∴ {b}^{loga} = {a}^{logb}\right)

y1log⁡5=xy\dfrac{1}{\log 5} = x

Replacing x→yx \to y and y→xy \to x

x1log⁡5=yx\dfrac{1}{\log 5} = y

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