Question

How to solve example 3 pls fast

Answer 1

7log(16/15) + 5log(25/24) + 3log(81/80) 

We have a formula i.e log(a/b) = log a - log b

= 7 log 16 - 7 log 15 + 5 log 25 - 5 log 24 + 3 log 81 - 3 log 80

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

We have a formula i.e log(x^3) = 3 log(x) and log(ab) = log a + log b

= 28 log 2 - 7 log 3 - 7 log 5 + 10log 5 - 15log 2 - 5log 3 + 12log 3 - 12log 2 - 3 log 5

= 13log 2 - 12 log 2 - 12log3 + 12log3 + 3log5 -3log5

= log 2