Solved: "For Exercise, solve the equations and inequalities. Write..."

ddaeeric

Answered question

2021-10-03

For Exercise, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation.

\log_{2} (3 x - 1) = \log_{2} (x + 1) + 3

Ezra Herbert

Skilled2021-10-04Added 99 answers

Property used:
Property 1:

\log_{2} (m) - \log_{2} (n) = \log_{2} (\frac{m}{n})

Now to simplifying the given equation:

\log_{2} (3 x - 1) = \log_{2} (x + 1) + 3

\log_{2} (3 x - 1) - \log_{2} (x + 1) = 3

\log_{2} (\frac{3 x - 1}{x + 1}) = 3

[Using Property 1.]
Now taking antilog 2 and solving:

(\frac{3 x - 1}{x + 1}) = 2^{3}

(3 x - 1) = 8 (x + 1)

(3 x - 1) = 8 x + 8

3 x - 8 x = 8 x + 1

- 5 x = 9

x = - \frac{9}{5}

Since,
The solution does not satisfy the given equation.
Hence there is no solution for

x \in R

Jeffrey Jordon

Expert2021-12-11Added 2605 answers

Answer is given below (on video)

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