1.

2log25/24 + 3log9/5 - 4log3/4​

Answer»

Given : 2log25/24 + 3log9/5 - 4log3/4​

To FIND : Simplify

Solution:

2 LOG ( 25 / 24)  + 3 log  (9/5)  - 4 log ( 3/4)

log ( a/ b) = log a - log b

= 2 log 25 - 2 log 24  + 3 log 9  - 3 log 5  - 4 log 3 + 4 log 4

= 2 log 5² - 2 log (8 x 3)   + 3 log 3²  - 3 log 5  - 4 log 3 + 4 log 2²

log aⁿ = n log a

=  4 log 5 - 2 log 8 - 2 log 3 + 6 log 3 - 3 log 5  - 4 log 3 + 8 log 2

=   log 5 - 2 log 2³ + 8 log 2

= log 5 - 6 log 2  + 8 log 2

= log 5   + 2 log 2

= log 5 + log 2 + log 2

= log ( 5 * 2)  + log 2

= log 10 + log 2

= 1 + log 2

= 1 + 0.3010

= 1.3010

2 log ( 25 / 24)  + 3 log  (9/5)  - 4 log ( 3/4) = 1 + log 2

Learn More:

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