K. C. Sinha Solutions for Chapter: Appendix II : Logarithm, Exercise 1: EXERCISE 9.1

Evaluate: ${\log }_{\sqrt{5}}\left(0.008\right)$

Prove that: ${\log }_3{\log }_2{\log }_{\sqrt{3}}81=1$.

Prove that ${\log }_{a}x\times {\log }_{b}y={\log }_{b}x\times {\log }_{a}y$.

Prove that $\log \left(1+2+3\right)=\log 1+\log 2+\log 3$.

Prove that: $2\log \left(1+2+4+7+14\right)=\log 1+\log 2+\log 4+\log 7+\log 14$

Prove that $\log 2+16\log \frac{16}{15}+12\log \frac{25}{24}+7\log \frac{81}{80}=1.$

If $a,b,c$ be in G.P., show that ${\log }_a\left(x\right),{\log }_b\left(x\right),{\log }_c\left(x\right)$ are in H.P.

Find the number of digits in ${\left(72\right)}^{15}$ without actual computation. Given $\log 2=0.301$ and $\log 3=0.477$.