Question

Вычислите log6 8 - log6 2+ log6 9

Answer 1

= log6_(8) + log6_(9) - log6_(2) = log6_(8*9/2)=log6_(72/2) = log6_(36) = 2

Answer 2

Log6 (8:2*9)=log6 36= 2

Answer 3

To compute the expression log6 8 - log6 2 + log6 9, we can use the properties of logarithms. The following rules will be useful:

1. log_b(x) - log_b(y) = log_b(x/y)
2. log_b(x) + log_b(y) = log_b(xy)

Applying these rules, we can simplify the expression step by step:

log6 8 - log6 2 + log6 9 = log6 (8/2) + log6 9 = log6 4 + log6 9

Now, we can use the rule log_b(x) + log_b(y) = log_b(xy):

log6 4 + log6 9 = log6 (4 * 9) = log6 36

Finally, we can write 36 as a power of 6:

log6 36 = log6 (6^2) = 2

Therefore, the value of the expression is 2.