G Tewani Solutions for Chapter: Logarithm and Its Applications, Exercise 2: DPP

There exist positive integers $A, B, C$ with no common factors greater than $1$, such that $A{\log }_{200}5+B{\log }_{200}2=C$, then $A+B+C=$

The value of $\left(2^{{\log }_{6}18}\right)\left(3^{{\log }_{6}3}\right)$ is:

If ${\log }_{\mathit{a}}b=2, {\log }_{\mathit{b}}c=2$ and ${\log }_{3}c=3+{\log }_{3}a$ then the value of $\frac{c}{ab}$ is

If ${\log }_{2}10=p, \frac{{\log }_{\mathit{e}}10}{{\log }_{\mathit{e}}7}=q$ and ${11}^r=10,$ then which one of the following expression is equivalent to ${\log }_{10}154?$

If $3^{{\left({\log }_{3}7\right)}^x}=7^{{\left({\log }_{7}3\right)}^x}$ then the value of $x$ will be

The value of $4^{5{\log }_{4\sqrt{2}}\left(3-\sqrt{6}\right)-6{\log }_8(\sqrt{3}-\sqrt{2})}$ is

The value of: $\frac{{81}^{\frac{1}{{\log }_{5}9}}+3^{\frac{3}{{\log }_{\sqrt{6}}3}}}{409}\left({\left(\sqrt{7}\right)}^{\frac{2}{{\log }_{25}7}}-{\left(\left(125\right)\right)}^{{\log }_{25}6}\right)$

The value of $6^{{\log }_{10}40}·5^{{\log }_{10}36}$ is: