If log(a) 2 + log(a) 4 = log (2) a^2, what is a?

log(a) 2 + log(a) 4 = log(2) a^2
.

We will use logarithm properties to find
a.

We know that log a + log b = log
a*b

==> log(a) 2 + log(a) 4 = log(a) 2*4 = log(a)
8

==> log(a) 8 = log(2)
a^2

Now we will
rewrite:

log(a) 8 = log(2) 8 / log(2) a = log(2) 2^3 /
log(2) a = 3/log(2) a

==> 3/log(2) a = log(2)
a^2

==> 3 = 2log(a) 2 * log(2)
a

==> 2[log(2) a)'^2 =
3

==> log(2) a = sqrt(3/2)=
sqrt(1.5)

==> Now we will rewrite into exponent
form.

==> a =
2^(sqrt(1.5)