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प्रश्न
Express the following as a single logarithm:
`2"log" (16)/(25) - 3 "log" (8)/(5) + "log" 90`
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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संबंधित प्रश्न
Given 2 log10 x + 1 = log10 250, find :
(i) x
(ii) log10 2x
If log 27 = 1.431, find the value of : log 300
Prove that:
log10 125 = 3(1 - log102).
Given `log_x 25 - log_x 5 = 2 - log_x (1/125)` ; find x.
Express the following in terms of log 2 and log 3: log 36
Express the following in terms of log 5 and/or log 2: log500
Express the following as a single logarithm:
`2"log"(15)/(18) - "log"(25)/(162) + "log"(4)/(9)`
If 2 log y - log x - 3 = 0, express x in terms of y.
If log 27 = 1.431, find the value of the following: log 9
Find the value of:
`("log"sqrt125 - "log"sqrt(27) - "log"sqrt(8))/("log"6 - "log"5)`
