find the numerical value of the log expression

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

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