Question

$\log \{{\left(\frac{b{c}^{-2}}{b^{-4}{c}^3}\right)}^{-3}÷{\left(\frac{b^{-1}c}{b^2{c}^{-3}}\right)}^5\}$.

Answer 1

$\log \{{\left(\frac{b{c}^{-2}}{b^{-4}{c}^3}\right)}^{-3}÷{\left(\frac{b^{-1}c}{b^2{c}^{-3}}\right)}^5\}=\log \{{\left(b^5{c}^{-5}\right)}^{-3}÷{\left(b^{-3}{c}^4\right)}^5\}=\log \left\{\frac{b^{-15}{c}^{15}}{b^{-15}{c}^{20}}\right\}=\log \left\{c^{-5}\right\}=-5\log c$