Question

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

Logarithms
ANSWERED
asked 2021-02-18

Solve the equations and inequalities. Write the solution sets to the inequalities in interval notation. \(\displaystyle{\log_{2}}{\left({3}{x}−{1}\right)}={\log_{2}}{\left({x}+{1}\right)}+{3}\)

Expert Answers (1)

2021-02-19

Property used:

Property 1:

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

Now to simplifying the given equation:

\(\log_{2}(3x-1)=\log_{2}(x+1)+3\) 

\(\log_{2}(3x-1)-\log_{2}(x+1)=3 \)

\(\log_{2}(\frac{3x-1}{x+1})=3\) [Using Property 1.]

Now taking antilog 2 and solving:

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

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

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

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

\(-5x=9\)

\(x=-\frac{9}{5}\)

Since,

The solution does not satisfy the given equation.

Hence there is no solution for \(x \in R\)

27
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours
...