Question

7Log10/9-2Log25/24+3Log81/80

Answer 1

Given 7 log(10/9) - 2 log(25/24) + 3 log(81/80)

We know that log(a/b) = log a - log b.

= log(10/9) - 2 log(25/24) + 3 log(81/80)
 
= 7(log 10 - log 3^2) - 2(log 25 - log 24) + 3(log 81 - log 80)

= 7(log 2 * 5 - 2 log 3) - 2(log 5^2 - log 3 * 2^3) + 3(log 3^4 - log 5 * 2^4)


We know that log(a + b) = log ab & log(a)^b = b log a.

= 7(log 2 + log 5 - 2 log 3) - 2(2 log 5 - log 3 - 3 log 2) + 3(4 log 3 - log 5 - 4 log 2)

= 7 log 2 + 7 log 5 - 14 log 3 - 4 log 5 + 2 log 3 + 6 log 2 + 12 log 3 - 3 log 5 - 12 log 2

= log 2.


Hope this helps!

Answer 2

Step-by-step explanation:

Hope it helps to you all.