Question

Express log2 6 + log2 7 as a single logarithm.

Answer 1

use the basic rule of logs for multiplication:

log a + log b = log a*b

Here you are adding two logs to the base 2, and your result will also be a log to the base 2.

log to the base 2 of 6 PLUS log to the base 2 of 7 results in:
"log to the base 2 of 6*7," or "log to the base 2 of 42."

Answer 2

Answer: The correct option is (C)
`\log_242.`

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

`E=\log_26+\log_27~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(I)`

We will be using the following logarithmic property :

`\log_ab+\log_ac=\log_a(bc)`

So, from expression (i), we get

`E=\log_26+\log_7=\log_2(6* 7)=\log_242.`

Thus, the required single logarithm is
`\log_242.`

Option (C) is CORRECT.