Question

find the value of log (225/32)-log(25/81)+log(64/729)

Answer 1

2log5-5log2-2log5-4log3+6log2-2log27

Answer 2

Here we have to find the value of log (225/32)-log(25/81)+log(64/729)
Solution:
log (225/32)-log(25/81)+log(64/729)
= log [ (5)². (3)² / (2)⁵ ] - log [ (5)² / (3)⁴ ] + log [ (2)⁶ / (3)⁶ ]
= log (5)² + log (3)² - log (2)⁵ - [ log (5)² - log (3)⁴ ] + log (2)⁶ - log (3)⁶
= log (5)² + log (3)² - log (2)⁵ - log (5)² + log (3)⁴ + log (2)⁶ - log (3)⁶
= 2.log5 + 2.log3 - 5.log2 - 2.log5 + 4.log3 + 6.log2 - 6.log3
= 2 (0.69897) + 2 (-0.32137) - 5 (0.30103) - 2 (0.69897) +4 (-0.32137) + 
6 (0.30103) -6 (-0.32137)
= 1.39794 - 0.64274 - 1.50515 - 1.39794 - 1.28548 + 1.80618 + 1.92822
= - 0.64274 - 1.50515 - 1.28548 + 1.80618 + 1.92822
= 0.30103
which is the required answer.
Hope it will help you. Thanks.