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

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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**

Given log a = 35 and log b= 20, the values of log (ab) , log (a/b) , log (1/a) and log (1/b) are:

log (ab) = log a + log b = 35 + 20 = 55

log (a/b) = log a - log b = 35 - 20 = 15

log (1/a) = 0- log a = 0 - 35 = -35

log (1/b) = 0 - log b = 0 - 20 = -20