Prove the following:
1. log_b² a².log_c² b².log_a² c²=1
2. Solve 213.768*4.434 whole divided by 6.321 using log table.

Dear Student,
Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{L}.\mathrm{H}.\mathrm{S}.={\log }_{{\mathrm{b}}^2}{\mathrm{c}}^2·{\log }_{{\mathrm{c}}^2}{\mathrm{a}}^2·{\log }_{{\mathrm{a}}^2}{\mathrm{b}}^2 \\ \mathrm{By} \mathrm{base} \mathrm{change} \mathrm{formula} {\log }_{\mathrm{p}}\mathrm{q}=\frac{{\log }_{10}\mathrm{q}}{{\log }_{10}\mathrm{p}} \\ \mathrm{Hence} \mathrm{we} \mathrm{have} \\ \mathrm{L}.\mathrm{H}.\mathrm{S}.=\frac{{\log }_{10}{\mathrm{c}}^2}{{\log }_{10}{\mathrm{b}}^2}.\frac{{\log }_{10}{\mathrm{a}}^2}{{\log }_{10}{\mathrm{c}}^2}.\frac{{\log }_{10}{\mathrm{b}}^2}{{\log }_{10}{\mathrm{a}}^2} \\ =\frac{\cancel{{\log }_{10}{\mathrm{c}}^2}}{\cancel{{\log }_{10}{\mathrm{b}}^2}}.\frac{\cancel{{\log }_{10}{\mathrm{a}}^2}}{\cancel{{\log }_{10}{\mathrm{c}}^2}}.\frac{\cancel{{\log }_{10}{\mathrm{b}}^2}}{\cancel{{\log }_{10}{\mathrm{a}}^2}} \\ =-1 =\mathrm{R}.\mathrm{H}.\mathrm{S}. \left(\mathrm{Hence} \mathrm{Proved}\right) \\ \mathrm{Please} \mathrm{ask} \mathrm{one} \mathrm{question} \mathrm{in} \mathrm{one} \mathrm{thread}. \end{gathered}$$

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