Question

Solve this:


7. Find the value of log₃₄₃ 49.

Answer 1

Dear student
$$\begin{gathered} {\log }_{343}\left(49\right) \\ ={\log }_{7^3}\left(7^2\right) \\ =\frac{1}{3}{\log }_7\left(7^2\right)\left[\because {\log }_{{\mathrm{a}}^{\mathrm{b}}}\left(\mathrm{x}\right)=\frac{1}{\mathrm{b}}{\log }_{\mathrm{a}}\left(\mathrm{x}\right)\right] \\ =\frac{2}{3}{\log }_7\left(7\right)\left[\because {\log }_{\mathrm{a}}\left({\mathrm{x}}^{\mathrm{b}}\right)={\mathrm{blog}}_{\mathrm{a}}\left(\mathrm{x}\right)\right] \\ =\frac{2}{3}\left[\because {\log }_{\mathrm{a}}\left(\mathrm{a}\right)=1\right] \end{gathered}$$
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