Question

Simplify it.

Log₃8\log₉16log₄10

Answer 1

Step-by-step explanation:

SOLUTION

$\frac{ log_{3}8}{ log_{9}16 \: log_{4}10 }$

$= > \frac{ log_{10}8 }{ log_{10}3 } . \frac{ log_{10}9 \: log_{10}4 }{ log_{10}16 \: log_{10}10 }$

(Changing all logs to base 10)

$= > \frac{ log_{10} {2}^{3}. \: log_{10} {3}^{2} . \: log_{10} {2}^{2} }{ log_{10}3 \: . \: log_{10} {2}^{4} . \: 1 }$

$= > \frac{(3 log_{10}2)(2 log_{10}3)(2 log_{10}2) }{( log_{10}3)(4 log_{10}2) }$

$= > 3 log_{10}2.$