Calculate the value of expression log 7 (2) + log 7 (14) - log 7 (4)

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

log 7(2) + log 7(14) -log 7(4)

log 7(2) + log 7 (2*7)  -log 7 (2^2)

We know that log xy= logx + log y

E=  log 7(2) + log 7 (2) + log 7(7) -2log 7(2)

Group similar:

   =  2log 7(2) + 1 -2log 7(2)

  Reduce similar:

E= 1

 

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

To calculate log7(2)+log7(14)-log7(4)

Solution:

log7(2)+log7(14)-log7(4)

=log7(2*14)-log7(4), as log k(a)+logk(b) = logk(ab)

= log7(2*14/4) , as logk(a)-logk(b) = logk(a/b).

= log7(7)

=1, as logk(k) = 1

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

First, we'll write the term log 7 (14) = log 7 (7*2).

We'll apply the product rule of logarithms:

log 7 (7*2) = log 7 (7) + log 7 (2)

log 7 (7*2) = 1 + log 7 (2)

We'll substitute the term log 7 (14) by it's result, 1 + log 7 (2).

The expression will become:

E = log 7 (2) + log 7 (14) - log 7 (4)

E = log 7 (2) + 1 + log 7 (2) - log 7 (4)

We'll group log 7 (2) + log 7 (2) = 2log 7(2)

We'll use the power rule:

2log 7(2) = log 7 (2^2) = log 7 (4)

E = log 7 (4) + 1 - log 7 (4)

We'll reduce the similar terms:

E = 1

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