Advertisements
Advertisements
प्रश्न
Express the following as a single logarithm:
`3"log"(5)/(8) + 2"log"(8)/(15) - (1)/(2)"log"(25)/(81) + 3`
Advertisements
उत्तर
`3"log"(5)/(8) + 2"log"(8)/(15) - (1)/(2)"log"(25)/(81) + 3`
= `3"log"(5)/(2^3) + 2"log"(2^3)/(3 xx 5) - (1)/(2)"log"(5^2)/(3^4) + 3"log"10`
= `3"log"5 - 3"log"2^3 + 2"log"2^3 - 2"log"3 - 2"log"5 - (1)/(2)"log"5^2 + (1)/(2)"log"3^4 + 3"log(2 xx 5)`
= `3"log"5 - 3 xx 3"log"2 + 2 xx 3"log"2 - 2"log"3 - 2"log"5 - (1)/(2) xx 2"log"5 + (1)/(2) xx 4"log"3 + 3"log"2 + 3"log5`
= 3log5 - 9log2 + 6log2 - 2log3 - 2log5 - log5 + 2log3 + 3log2 + 3log5
= 3log5
= log53
= log125.
APPEARS IN
संबंधित प्रश्न
If log102 = a and log103 = b ; express each of the following in terms of 'a' and 'b': log 2.25
Given: log3 m = x and log3 n = y.
Express 32x - 3 in terms of m.
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 54
Express the following in terms of log 2 and log 3: log 144
Express the following in terms of log 2 and log 3: `"log" root(3)(144)`
If 2 log x + 1 = 40, find: x
If log1025 = x and log1027 = y; evaluate without using logarithmic tables, in terms of x and y: log103
If x2 + y2 = 7xy, prove that `"log"((x - y)/3) = (1)/(2)` (log x + log y)
