For Exercise, solve the equations and inequalities. Write the solution sets to t

ddaeeric

ddaeeric

Answered question

2021-10-03

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

Answer & Explanation

Ezra Herbert

Ezra Herbert

Skilled2021-10-04Added 99 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.
Jeffrey Jordon

Jeffrey Jordon

Expert2021-12-11Added 2605 answers

Answer is given below (on video)

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