Show-that-log-2-5-log-4-3-log-25-16-log-2-3-

Question Number 132368 by otchereabdullai@gmail.com last updated on 13/Feb/21

Show that \log_{2} 5 . \log_{4} 3 . \log_{25} 16 = \log_{2} 3

Answered by mr W last updated on 13/Feb/21

g e n e r a l l y \log_{a} b = \frac{\log_{c} b}{\log_{c} a}

\log_{2} 5 . \log_{4} 3 . \log_{25} 16

= \frac{\log_{2} 5}{\log_{2} 2} \times \frac{\log_{2} 3}{\log_{2} 4} \times \frac{\log_{2} 16}{\log_{2} 25}

= \frac{\log_{2} 5}{\log_{2} 2} \times \frac{\log_{2} 3}{{2 \log}_{2} 2} \times \frac{{4 \log}_{2} 2}{2 \log_{2} 5}

= \frac{1}{1} \times \frac{\log_{2} 3}{2} \times \frac{4}{2}

= \log_{2} 3

Commented by otchereabdullai@gmail.com last updated on 13/Feb/21

you are always my prof! If something

is more than blessing God should give

it to you

Commented by mr W last updated on 14/Feb/21

G o d b l e s s y o u t o o!

Facebook Tweet Pin