Solve: \log_2(2x+1)-\log_2(x-2)=1

Dottie Parra

Dottie Parra

Answered question

2021-10-29

Solve: log2(2x+1)log2(x2)=1

Answer & Explanation

Laaibah Pitt

Laaibah Pitt

Skilled2021-10-30Added 98 answers

Step 1
Logarithms and exponential functions are considered to be the inverses of each other as one can always represent one function in other functions form.
For example : a=yx . Taking log both sides, we get loga=xlogy.
Therefore, we can express log in exponential forms and exponents in logarithms form.
There are different properties of logarithms when we solve equations related to them and hence those are to be kept in mind while solving.
Step 2
Using properties of logarithms : logablogac=loga(bc)
Applying this property on the original equation.
log2(2x+1)log2(x2)=1
log2(2x+1x2)=1
2x+1x2=21
2x+1x2=2
2x+1=2x4
Since, this can never be equal, the solution for the equation does not exist.
The system has no solution.

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