What is the inverse of the function y = 5log x

  1. x=51logy
  2. x=y1log5
  3. x = 5 log y
  4. none of these

Answer (Detailed Solution Below)

Option 2 : x=y1log5
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Detailed Solution

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CONCEPT:

Let f: A → B be one-one and onto (bijective) function. Then f-1 exists which is a function f-1: B → A, which maps each element b ∈ B with an element a ∈ A such that f(a) = b is called the inverse function of f: A → B.

Methods to find inverse:

Let f : A → B be a bijective function.

Step – I Put f (x) = y

Step – II Solve the equation y = f (x) to obtain x in terms of y.

Interchange x and y to obtain the inverse of the given function f

CALCULATION:

Given: y = 5log x

Here we have to find the inverse of the given function

By applying log to base 5 on both sides of y = 5log x we get,

⇒ log5y=log5(5logx)

⇒ log5y=logx

⇒ logylog5=logx

⇒ log[y1log5]=logx

⇒ x=y1log5

Hence, option B is the correct answer.

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