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Express log2 6 + log2 7 as a single logarithm. PLEASEE HELP!

Alog2 7/6
Blog2 6/7
Clog2 √ 42
Dlog2 42

Verified Answer :

Answer:  The correct option is (D) \(\log_242.\)

Step-by-step explanation:  We are given to write the following logarithmic expression as a single logarithm :

\(E=\log_26+\log_27.\)

We will be using the following property of logarithm :

\(\log_ab+\log_ac=\log_abc.\)

For the given expression, we have

\(E\\\\=\log_26+\log_27\\\\=\log_2(6\times7)\\\\=\log_242.\)

Thus, the required single logarithm is \(\log_242.\)

Option (D) is CORRECT.

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