Question

2log25/24 + 3log9/5 - 4log3/4​

Answer 1

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

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If x=log(a+b) y=log(a-b) z=log(a²-b²). Then what is the relation ...

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Answer 2

Step-by-step explanation:

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

•  So we can write this as  
•            2 log (25/24) + 3 log (9/5) – 4 log (3/4)
•               log (25/24)^2 + log (9/5)^3 – log (3/4)^4
•               log (5^2 / 2^3 x 3)^2 + log (3^2 / 5)^3 – log (3 / 2^2)^4
•               log (5^4 / 2^6 x 3^2) + log (3^6 / 5^3) – log 3^4 / 2^8
•              log [(5^4 / 2^6 x 3^2) x 3^6 / 5^3 x 2^8 / 3^4]
•                log [ 5 x 2^2]
•                log 20 to base 10
•                = 1.301

Reference link will be

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