If log a = 35 and log b= 20 calculate : log (ab) , log (a/b) , log (1/a) and log (1/b)

Given that:

log a =
35

log b = 20

We need to
calculate the values of the following:

1.log
(ab)

We will use the logarithm properties to
solve.

We know that log a + log b  = log
ab

==> log ab = 35 + 20 =
55

==> log ab =
55

2. log
a/b

We know that: log a - log b = log
a/b

==> log a/b = 35 -20 =
15

==> log a/b =
15

log
(1/a)

Let us rewrite as a negative
exponent.

==> log 1/a = log
a^-1

Now we know that log a^b = b*log
a

==> log a^-1 = - log a = -
35

==> log (1/a) =
-35

4. log (1/b) = log b^-1 = -1*log b =
-1*20 = -20

==> log (1/b) =
-20