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Question
Answer the following:
Find value of `(3 + log_10 343)/(2 + 1/2 log_10 (49/4) + 1/2 log_10 (1/25)`
Solution
`(3 + log_10 343)/(2 + 1/2 log_10 (49/4) + 1/2 log_10 (1/25)`
= `(3 + log_10 7^3)/(2 + log_10 (49/4)^(1/2) + log_10 (1/25)^(1/2)`
= `(3 + 3.log_10 7)/(2 + log_10 7/2 + log_10 1/5)`
= `(3(1 + log_10 7))/(2 + log_10 (7/2 xx 1/5)`
= `(3(1 + log_10 7))/(2 + log_10 (7/10))`
= `(3(1 + log_10 7))/(2 + log_10 7 - log_10 10)`
= `(3(1 + log_10 7))/(2 + log_10 7 - 1)` ...[∵ loga a = 1]
= `(3(1 + log_10 7))/(1 + log_10 7)`
= 3
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