If log 25=a , log225=b, prove that log (1\9^2)+log (1\2250)=2a-3b-1
Answers
Given : log 25=a , log225=b,
To find : show that log (1/9²)+log (1/2250) = 2a-3b-1
Solution:
log 25=a
log225=b
=> log 25 * 9 = b
=> log 25 + log 9 = b
=> a + log 9 = b
=> b - a = log 9
log (1/9²)+log (1/2250)
= log 1 - log 9² + log 1 - log 2250
= 0 - 2 log 9 + 0 - log (225 * 10)
= - 2(b - a) - (log 225 + log 10)
= - 2b + 2a - (b + 1)
= - 2b + 2a - b - 1
= 2a - 3b - 1
= RHS
QED
Hence proved
log (1/9²)+log (1/2250) = 2a-3b-1
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