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प्रश्न
Simplify the following:
`3"log" (32)/(27) + 5 "log"(125)/(24) - 3"log" (625)/(243) + "log" (2)/(75)`
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उत्तर
`3"log" (32)/(27) + 5 "log"(125)/(24) - 3"log" (625)/(243) + "log" (2)/(75)`
= `3"log" (2^5)/(3^3) + 5"log"(5^3)/(2^3 xx 3) - 3"log"(5^4)/(2 xx 3^4) + "log"(2)/(3 xx 5^2)`
= 3 log 25 − 3 log 33 + 5 log 53 − 5 log 23 − 5 log 3 − 3 log 54 + 3 log 2 + 3 log 34 + log 2 − log 3 - log 52
= 3 x 5 log 2 − 3 x 3 log 3 + 5 x 3 log 5 − 5 x 3 log 2 − 5 log 3 − 3 x 4 log 5 + 3 log 2 + 3 x 4 log 3 + log 2 − log 3 − 2 log 5
= 15 log 2 − 9 log 3 + 15 log 5 − 15 log 2 − 5 log 3 − 12 log 5 + 3 log 2 + 12 log 3 + log 2 − log 3 − 2 log 5
= log 5 + log 2
= log (5 x 2)
= log 10
= 1.
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