Embibe Experts Solutions for Chapter: Logarithm and its Applications, Exercise 1: Exercise 1

What is the value of ${\log }_{\mathrm{y}}{x}^5{\log }_{\mathrm{x}}{y}^2{\log }_{\mathrm{z}}{z}^3$ ?

If ${\log }_{8}m+{\log }_8\frac{1}{6}=\frac{2}{3},$ then $m$ is equal to

What is the value of ${\log }_7{\log }_7$$\sqrt{7\sqrt{7\sqrt{7}}}$ equal to?

What is the value of ${\log }_{9}27+{\log }_{8}32$?

If $x+{\log }_{10}\left(1+2^x\right)=x{\log }_{10}5+{\log }_{10}6$, then $x$ is equal to

If $(0.2{)}^x=2$ and ${\log }_{10}2=0.3010,$ then what is the value of $x$ to the nearest tenth?

If $n=\left(2017\right)!,$ then what is $\frac{1}{{\log }_{2}n}+\frac{1}{{\log }_{3}n}+\frac{1}{{\log }_{4}n}+\dots +\frac{1}{{\log }_{2017}n}$ equal to?

If $x+{\log }_{15}\left(1+3^x\right)=x{\log }_{15}5+{\log }_{15}12,$ where $x$ is an integer, then what is $x$ equal to?