Solve the equation: \log_{3}(2x+1)=\log_{3}(5x)+2.

CheemnCatelvew

CheemnCatelvew

Answered question

2021-02-21

Solve the equation: log3(2x+1)=log3(5x)+2.

Answer & Explanation

Bentley Leach

Bentley Leach

Skilled2021-02-23Added 109 answers

Step 1
Given equation:
log3(2x+1)=log3(5x)+2
Step 2
Now
Apply log rule: logc(a)logc(b)=logc(ab)
Apply log rule: logc(a)=ya=cy
Therefore,
log3(2x+1)=log3(5x)+2
log3(2x+1)log3(5x)=2
log3(2x+15x)=2
2x+15x=32
2x+15x=9
2x+1=9×5x
2+1=45x
1=45x-2x
43x=1
x=143
To verify the solution, put x=143 in the given equation:
log3(2x+1)=log3(5x)+2
log3(2x+1)log3(5x)=2
log3(2x+15x)=2
Put x=143
log3(2×143+15×143)=2
log3(455)=2
log3(9)=2
log3(32)=2
Apply log rule: logc(cx)=x
2=2
LHS=RHS
Hence,
The required solution is x=143

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