O P Malhotra, S K Gupta and, Anubhuti Gangal Solutions for Exercise 2: Exercise

If ${\log }_2 12-{\log }_2 2+{\log }_{2 }5$ as a single logarithm is equal to ${\log }_2 k$, then find the value of $k$.

Simplify without using tables: $\frac{{\log }_{40}1000 }{{\log }_{40}100}$

Simplify without using tables: ${\log }_2 8$

Prove that: $\log \sqrt[3]{6\frac{2}{9}}=\frac{1}{3}\left(\log 7-2 \log 3\right)+\log 2$

Solve: ${\log }_{10}n+{\log }_{10}5=1$

Simplify: ${\log }_{10}5+{\log }_{10}2$

Simplify: ${\log }_{10}4+{\log }_{10}5-{\log }_{10}2$

Simplify: $2{\log }_{10}5+{\log }_{10}8-\frac{1}{2}{\log }_{10}4$