If log₁₀2 = a & log₁₀3 = b, then express each of the following in terms of a & b :-
(i): log₁₀5.4
(ii): log₁₀25/8

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Please find below the solution to the asked query:

Given :  log₁₀ 2 = a  and  log₁₀ 3 = b 
i ) log₁₀ 5.4
$$\begin{gathered} \Rightarrow {\log }_{10}\left(\frac{54}{10}\right) \\ \Rightarrow {\log }_{10} 54 - {\log }_{10} 10 ( \mathrm{We} \mathrm{know} \log \left(\frac{\mathrm{a}}{\mathrm{b}}\right) = \log \mathrm{a} - \log \mathrm{b} ) \\ \Rightarrow {\log }_{10} \left(2 \times 27 \right) - {\log }_{10} 10 \\ \Rightarrow {\log }_{10} 2 + {\log }_{10} 27 - {\log }_{10} 10 ( \mathrm{We} \mathrm{know} \log \left(\mathrm{a} \times \mathrm{b}\right) = \log \mathrm{a} + \log \mathrm{b} ) \\ \Rightarrow {\log }_{10} 2 + {\log }_{10} 3^3 - {\log }_{10} 10 \\ \Rightarrow {\log }_{10} 2 + 3 {\log }_{10} 3 - {\log }_{10} 10 ( \mathrm{We} \mathrm{know} \log {\mathrm{a}}^{\mathrm{b}} = \mathrm{b} \log \mathrm{a} ) \\ \mathbf{\Rightarrow }\mathbf{a}\mathbf{ }\mathbf{ }\mathbf{+}\mathbf{ }\mathbf{3}\mathbf{ }\mathbf{b}\mathbf{ }\mathbf{ }\mathbf{-}\mathbf{ }\mathbf{1}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{(}\mathbf{ }\mathbf{Ans}\mathbf{ }\mathbf{)} \end{gathered}$$

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