Answer:
9
Step-by-step explanation:
I'm going to solve this question by expanding the logarithm (note that you can also solve this equation by solving for a, b, and c)
We know the following
[tex]log(ab)=log(a)+log(b)[/tex]
Which means we can split the numerator into
[tex]log(b^{1/2})+log(c^{3/2})[/tex]
We also know that
[tex]log(a^{x})=x*log(a)[/tex]
Which means that we can rewrite the following as
[tex]\frac{log(b)}{2}+\frac{3log(c)}{2}[/tex]
We can evaulate this and get
-1+12= 11
for the numerator
Now we need to take care of the denominator
we know the following
[tex]log(\frac{x}{y})=log(x)-log(y)[/tex]
which means that we have
11-2log(a)
solve and get
11-2
9
