simplify-log-3-11-log-11-13-log-13-15-log-15-27-log-27-81-please-i-need-help-

Question Number 141469 by otchereabdullai@gmail.com last updated on 19/May/21

simplify

(\log_{3} 11) (\log_{11} 13) (\log_{13} 15) (\log_{15} 27) (\log_{27} 81)

please i need help

Answered by bramlexs22 last updated on 19/May/21

\log_{3} 11 . \log_{11} 13 = \log_{3} 13

\log_{13} 15 . \log_{15} 27 = \log_{13} 27

\Rightarrow \log_{3} (13) . \log_{13} (27) = \log_{3} (27)

\Rightarrow \log_{3} (27) . \log_{27} (81) = \log_{3} (81) = 4

Commented by otchereabdullai@gmail.com last updated on 19/May/21

God bless you sir!

Answered by Rasheed.Sindhi last updated on 19/May/21

\frac{\log 11}{\log 3} . \frac{\log 13}{\log 11} . \frac{\log 15}{\log 13} . \frac{\log 27}{\log 15} . \frac{\log 81}{\log 27}

= \frac{\log 81}{\log 3} = \log_{3} 81 = 4

Commented by otchereabdullai@gmail.com last updated on 19/May/21

God bless you sir!

Answered by mr W last updated on 19/May/21

\log_{a} b = \frac{\ln b}{\ln a}

(\log_{3} 11) (\log_{11} 13) (\log_{13} 15) (\log_{15} 27) (\log_{27} 81)

= \frac{\ln 11}{\ln 3} \times \frac{\ln 13}{\ln 11} \times \frac{\ln 15}{\ln 13} \times \frac{\ln 27}{\ln 15} \times \frac{\ln 81}{\ln 27}

= \frac{\ln 81}{\ln 3}

= \frac{\ln 3^{4}}{\ln 3}

= \frac{4 \times \ln 3}{\ln 3}

= 4

Commented by otchereabdullai@gmail.com last updated on 19/May/21

God bless you prof