Question

log27=5 log 3_ log9​

Answer 1

Answer:

How I can solve log5 base3 × log 27 base 25?

[math]\text{Use change of base for } 2^{nd} \text{ term: } \log_b(x) = \frac{\log_a(x)}{\log_a(b)}[/math]

[math]\log_3(5) \times \log_{25}(27)[/math]

[math]= \log_3(5) \times \dfrac{\log_{3}(27)}{\log_{3}(25)}[/math]

[math]= \log_3(5) \times \dfrac{\log_{3}\left(3^3\right)}{\log_{3}\left(5^2\right)}[/math]

[math]= \log_3(5) \times \dfrac{3}{2\log_{3}(5)}[/math]

[math]= \boldsymbol{\dfrac{3}{2}}[/math]

Answer 2

Hope it is useful for you....