Advertisements
Advertisements
Question
Express the following as a single logarithm:
log 144 - log 72 + log 150 - log 50
Advertisements
Solution
log 144 - log 72 + log 150 - log 50
= log (24 x 32) - log (23 x 32) + log (2 x 3 x 52) - log (2 x 52)
= log 24 + log 32 - {log 23 + log 32} + log 2 + log 3 + 52 - {log 2 + log 52}
= 4 log 2 + 2 log 3 - 3 log 2 - 2 log 3 + log 2 + log 3 + 2 log 5 - log 2 - 2 log 5
= log 2 + log 3
= log (2 x 3)
= log 6.
APPEARS IN
RELATED QUESTIONS
If log102 = a and log103 = b ; express each of the following in terms of 'a' and 'b': log 2.25
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 144
Express the following in terms of log 2 and log 3: log128
Express the following in terms of log 5 and/or log 2: log160
Express the following in terms of log 2 and log 3: `"log" root(4)(648)`
Express the following as a single logarithm:
`2"log"(15)/(18) - "log"(25)/(162) + "log"(4)/(9)`
Express the following as a single logarithm:
`"log"(81)/(8) - 2"log"(3)/(5) + 3"log"(2)/(5) + "log"(25)/(9)`
If log x = A + B and log y = A-B, express the value of `"log" x^2/(10y)` in terms of A and B.
If log 8 = 0.90, find the value of each of the following: `"log"sqrt(32)`
