Question

The function h is given by 2 h x( ) = log2 (x^2+2). for what positive value of x does h(x) = 3 ?

Answer 1

Positive value of x for the given function 2h(x) = log₂(x² +2) is equal to √62.

As given in the question,

Function h is given by : 2h(x) = log₂(x² +2)

Using the definition of logarithm function

aˣ = y

⇒x= logₐy

For h(x) =3, Apply definition of logarithm function we get,

2× 3 = log₂(x² +2)

⇒6= log₂(x² +2)

⇒2⁶ = x² +2

⇒x² = 64-2

⇒x²= 62

⇒x = √62

Therefore, positive value of x for the given function 2h(x) = log₂(x² +2) is equal to √62.

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