The numerical value is -9
EXPLANATION
Given:
[tex]\log \frac{b^3c^3}{\sqrt[]{a^3}}[/tex]
This can be re-written as;
[tex]\log \frac{b^3c^3}{a^{\frac{3}{2}}}[/tex]
Applying the laws of logarithm
[tex]\log b^3+\log c^3-\log a^{\frac{3}{2}}[/tex]
[tex]3\log b+3\log c-\frac{3}{2}\log a[/tex]
From the values given;
loga =10 logb=11 logc=-9
Substitute
[tex]3(11)+3(-9)-\frac{3}{2}(10)[/tex][tex]=33-27-15[/tex][tex]=-9[/tex]
