Use [tex]\log_b 2 = 0.693[/tex] and/or [tex]\log_b 7 = 1.946[/tex] to find [tex]\log_b 14[/tex].

W e kn o w : l o g a ​ ( b ⋅ c ) = l o g a ​ b + l o g a ​ c t h ere f ore : l o g b ​ 14 = l o g b ​ ( 2 ⋅ 7 ) = l o g b ​ 2 + l o g b ​ 7 = 0.693 + 1.946 = 2.639

Answered by Anonymous | 2024-06-10

lo g b ​ 14 = 2.639 .
Given that:

lo g b ​ 2 = 0.693
lo g b ​ 7 = 1.946

Using logarithmic properties, we know that:
lo g b ​ ( ab ) = lo g b ​ a + lo g b ​ b .
So, we can rewrite lo g b ​ 14 as lo g b ​ ( 2 × 7 ) .
Substituting the given values, we get:
lo g b ​ 14 = lo g b ​ ( 2 × 7 ) = lo g b ​ 2 + lo g b ​ 7 = 0.693 + 1.946
Now, we can add these values together:
lo g b ​ 14 = 0.693 + 1.946 = 2.639
So, lo g b ​ 14 = 2.639 .
Question:
Given that lo g b ​ 2 = 0.693 and lo g b ​ 7 = 1.946 , use these values to find lo g b ​ 14 .

Answered by JoanBlondell | 2024-06-26

Using the properties of logarithms, lo g b ​ 14 can be computed as the sum of lo g b ​ 2 and lo g b ​ 7 . This gives us the final result, lo g b ​ 14 = 2.639 .
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Answered by JoanBlondell | 2024-12-26