If 10^a=5, 10^b=6, what is the value of 10^(2a+b). Please use log.

By using log.

We will rewrite
exponent into logarithm forms.

10^a = 5 ==> log 5 =
a...........(1)

10^b = 6 ==> log 6 =
b...........(2)

Now we will find the value of
10^(2a+b)

==> Let 10^(2a+b) =
x

==> we will take log to both
sides.

==> log 10^(2a+b) = log
x

==> 2a+ b= log x

==>
log x = 2*log 5 + log 6

==> Now we will use logarithm
properties to solve.

==> We know that alog b = log
b^a

==> log x = log 5^2 + log
6

==> log x = log 25 + log 6

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

==> log x = log
25*6

==> log x = log
150

==> x =
150

==> 10^(2a+b) =
150