Solve the equations and inequalities. Write the solution sets to the inequalities in interval notation. log2(3x−1)=log2(x+1)+3

Dottie Parra

Dottie Parra

Answered question

2021-02-18

Solve the equations and inequalities. Write the solution sets to the inequalities in interval notation. log2(3x1)=log2(x+1)+3

Answer & Explanation

Laith Petty

Laith Petty

Skilled2021-02-19Added 103 answers

Property used:

Property 1:

log2(m)log2(n)=log2(mn)

Now to simplifying the given equation:

log2(3x1)=log2(x+1)+3 

log2(3x1)log2(x+1)=3

log2(3x1x+1)=3 [Using Property 1.]

Now taking antilog 2 and solving:

(3x1x+1)=23

(3x1)=8(x+1)

(3x1)=8x+8

3x8x=8x+1

5x=9

x=95

Since,

The solution does not satisfy the given equation.

Hence there is no solution for xR

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