Question

log 2 + 16 log 16÷15 + 12 log 25÷24 + 7 log 81÷80

Answer 1

hello users ......

we have to solve 
Log 2 + 16 log 16/15 + 12 log 25/24 + 7 log 81/80 = ?

solution:-
we know that :
log mn = log m + log n 
and 
log m/n = log m - log n 
and 
log $m^{n}$ = n log m
and 
4 power of 2  = 16 
3 power of 2 = 8
4 power of 3 = 81
2 power of 5 = 25 

here,
Log 2 + 16 log 16/15 + 12 log 25/24 + 7 log 81/80 
= log 2 + 16( log 16 - log 15 ) + 12 ( log 25 - log 24) + 7 ( log 81 - log 80 )

=log 2 + 16 log 16 - 16 log 15 + 12 log 25 - 12 log 24 + 7 log 81 -7 log 80 

=log 2 + 16 log 16 - 16 log 5×3 + 12 log 25 - 12 log 8×3 + 7 log 81 -7 log 10 × 8

= log 2 + 16 × 4 log 2 - 16(log 5 + log 3) + 12×2 log 5 - 12 (log 8 +log 3)
       + 7× 4 log 3 - 7 (log 10 + log 8 ) 

=log 2 + 64 log 2 - 16 log 5 - 16 log 3 + 24 log 5 - 12 log 8 - 12 log 3 +28 log 3 - 7 log 10 - 7 log 8

= log 2 + 64 log 2 - 16 log 5 - 16 log 3 + 24 log 5 - 12×3 log 2 - 12 log 3 +28 log 3 - 7 log 10 - 7×3 log 2

= log 2 + 64 log 2 - 16 log 5 - 16 log 3 + 24 log 5 - 36 log 2 - 12 log 3 +28 log 3 - 7 log 10 - 21 log 2

= 65 log 2 - 57 log 2 + 28 log 3 - 28 log 3 + 24 log 5  - 16 log 5 - 7 log 10

=8 log 2  +8 log 5 - 7 log 10 

=8 ( log 5 + log 2) - 7 log 10

=8 log 5 × 2 - 7 log 10 

= 8 log 10 - 7 log 10 

= log 10  or = 1 answer 

❈❈ hope it helps ❈❈

Answer 2

Answer:

1

Step-by-step explanation:

I have connected my solution for ur concern