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प्रश्न
Express the following as a single logarithm:
`2"log" (16)/(25) - 3 "log" (8)/(5) + "log" 90`
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उत्तर
`2"log" (16)/(25) - 3 "log" (8)/(5) + "log" 90`
= `2 "log" (2^4)/(5^2) - 3 "log" (2^3)/(5) + "log" (2 xx 5 xx 3^2)`
= 2log 24 - 2 log 52 - 3{log 23 - log 5} + log 2 + log 5 + log 32
= 2 x 4 log 2 - 2 x 2 log 5 - 3 x 3 log 2 + 3 log 5 + log 2 log 5 + 2 log 3
= 8 log 2 - 4 log 5 - 9 log 2 + 3 log 5 + log 2 + log 5 + 2 log 3
= 2 log 3
= log 32
= log 9.
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