Solve the logarithmic equation \log_3(x+3)=\log_3(3x-5)

permaneceerc

permaneceerc

Answered question

2021-10-28

Solve the logarithmic equation
log3(x+3)=log3(3x5)

Answer & Explanation

Sadie Eaton

Sadie Eaton

Skilled2021-10-29Added 104 answers

Step 1
Given logarithmic equation is:
log3(x+3)=log3(3x5)
Step 2
Using the equality property of logarithms:
Inside the logarithms will be equivalent to each other, if their bases are equal.
log3(x+3)=log3(3x5)
In the above equation, both sides have the same base log3, so we will remove the log3 from both sides and rewrite the equation
(x+3)=(3x5)
3xx=3+5
2x=8
x=82
x=4
Step 3
Therefore, the solution of the given equation is x=4 .

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