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

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