Write the expression as a logarithm: 2\log_2(x-3)+\log_2(2x+3)

Sherry Becker

Sherry Becker

Answered question

2021-11-06

Write the expression as a logarithm:
2log2(x3)+log2(2x+3)

Answer & Explanation

Louis Gregory

Louis Gregory

Beginner2021-11-07Added 14 answers

Step 1
Simplify the logarithmic expression as follows.
2log2(x3)+log2(2x+3)=log2((x3)2)+log2(2x+3)   (ac(b)=logc(ba))
Step 2
Use the product rule for logarithms.
When adding the logs with same base, keep the log and base and multiply the elements as follows.
2log2(x3)+log2(2x+3)=log2((x3)2(2x+3))    (logc(a)+logc(b)=logc(ab))
Step 3
Answer:
The expression can be written as log2((x3)2(2x+3))

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