Question

Which of the following is equal to log 6

a) log 2 + log 3
b) log 2 -  log 3
c) 2 log 2 + log 3
d)2 log 2  - log 3

Answer 1

Note: Log A + Log b = Log(A*B)

a) log 2 + log 3 = log (2*3)
= log6.

Answer =a.

Answer 2

`log_ab+log_ac=log_a(b\cdot c)\\\\log_ab-log_ac=log_a(b:c)\\\\log_ab^c=c\cdot log_ab`



`\boxed{a)\ log2+log3=log(2\cdot3)=log6}\\\\b)\ log2-log3=log(2:3)=log(2)/(3)\\\\c)\ 2log2+log3=log2^2+log3=log4+log3=log(4\cdot3)=log12\\\\d)\ 2log2-log3=log2^2-log3=log4-log3=log(4:3)=log(4)/(3)`