Question

3log2/9+2log15/2-log25/81=log2

Answer 1

firstly, remember the concepts using logarithm,

• log m + log n = log mn......(1)
• log m - log n = log (m/n) .....(2)
• a log m = log(m^a).....(3)

now, 3log(2/9) = log(2/9)³ [ from equation (3) ]

=log(2³/9³) log(8/729)

similarly, 2log(15/2) = log(15/2)²

= log(15²/2²) = log(225/4)

now, LHS = 3log(2/3) + 2log(15/2) - log(25/81)

= log(8/729) + log(225/4) - log(25/81)

= log(8/729 × 225/4) - log(25/81) [ from equation (1) ]

= log(450/729) - log(25/81)

= log[(450/729)/(25/81)] [ from equation (2) ]

= log(450/729 × 81/25)

= log(18/9)

= log(2) = RHS

Answer 2

Step-by-step explanation:

log(2)= RHS

hope this helps you