Question

the value of log 27 to the base 9 - log 9 to the base 27​

Answer 1

Answer:

General formulas

$log_{ {a}^{m} }( {b}^{n} ) = \dfrac{n}{m} \times log_{b}(a)$

$log_{ \alpha }( \alpha ) = 1$

Above formulas ⬆️⬆️⬆️⬆️

will be used to find the value of given expression.

Now,

we have to find the value of,

$log_{9}(27) - log_{27}(9) \\ \\ = log_{ {3}^{2} }( {3}^{3} ) - log_{ {3}^{3} }( {3}^{2} ) \\ \\ = \frac{3}{2} log_{3}(3) - \frac{2}{3} log_{3}(3) \\ \\ = \frac{3}{2} - \frac{2}{3} \\\\ = \frac{9 - 4}{6} \\ \\ = \frac{5}{6}$

value of given expression will be

5/6.

Answer 2

SOLN REFERS TO THE ATTACHMENT..