If log a = 12 and log b = 3Find the value of log (a^2* b^3)^6

Given that :

log a =
12

log b= 3

We need to find
the value of the expression :

log
(a^2*b^3)^6

First we know that log a^b= b*log
a.

==> log (a^2*b^3)^6 = 6*log
(a^2*b^3)

Now we know that log ab = log a + log
b

==> log (a^2*b^3)^6 = 6[ log a^2 + log
b^3]

                                     = 6 [ 2log a +
3log b}

Now we simplified as
follows.

==> log (a^2*b^3)^6 = 6[ 2log a + 3log
b]

We will substitute with the given
values.

==> log (a^2*b^3)^6 = 6( 2*12 +
3*3)

                                      =
6(24+9)

                                       =
6*33

                                       =
198

Then the value of log (a^2*b^3)^6 =
198.