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

Dottie Parra 2021-02-18 Answered

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

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Expert Answer

Laith Petty
Answered 2021-02-19 Author has 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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