Which of the following is equal to [tex]\log 6[/tex]?

A. [tex]\log 2 + \log 3[/tex]
B. [tex]\log 2 - \log 3[/tex]
C. [tex]2 \log 2 + \log 3[/tex]
D. [tex]2 \log 2 - \log 3[/tex]

l o g a ​ b + l o g a ​ c = l o g a ​ ( b ⋅ c ) l o g a ​ b − l o g a ​ c = l o g a ​ ( b : c ) l o g a ​ b c = c ⋅ l o g a ​ b
a ) l o g 2 + l o g 3 = l o g ( 2 ⋅ 3 ) = l o g 6 ​ b ) l o g 2 − l o g 3 = l o g ( 2 : 3 ) = l o g 3 2 ​ c ) 2 l o g 2 + l o g 3 = l o g 2 2 + l o g 3 = l o g 4 + l o g 3 = l o g ( 4 ⋅ 3 ) = l o g 12 d ) 2 l o g 2 − l o g 3 = l o g 2 2 − l o g 3 = l o g 4 − l o g 3 = l o g ( 4 : 3 ) = l o g 3 4 ​

Answered by Anonymous | 2024-06-10

Note: Log A + Log b = Log(A*B)
a) log 2 + log 3 = log (2*3) = log6.
Answer =a.

Answered by olemakpadu | 2024-06-10

The only option equal to lo g 6 is option A, which states lo g 2 + lo g 3 . This is because the property of logarithms allows us to express the sum of logarithms as the logarithm of a product. Thus, lo g 2 + lo g 3 = lo g ( 2 ⋅ 3 ) = lo g 6 .
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Answered by Anonymous | 2024-09-05