Advertisements
Advertisements
Question
Express the following as a single logarithm:
`"log"(81)/(8) - 2"log"(3)/(5) + 3"log"(2)/(5) + "log"(25)/(9)`
Advertisements
Solution
`"log"(81)/(8) - 2"log"(3)/(5) + 3"log"(2)/(5) + "log"(25)/(9)`
= `"log"(3^4)/(2^3) - 2"log"(3)/(5) + 3"log"(2)/(5) + "log"(5^2)/(3^2)`
= log34 - log23 - 2log3 + 2log5 + 3log2 - 3log5 + log52 - log32
= 4log3 - 3log2 - 2log3 + 2log5 + 3log2 - 3log5 + 2log5 - 2log3
= log5.
APPEARS IN
RELATED QUESTIONS
Given 2 log10 x + 1 = log10 250, find :
(i) x
(ii) log10 2x
Prove that:
log10 125 = 3(1 - log102).
Express the following in terms of log 5 and/or log 2: log125
Write the logarithmic equation for:
F = `"G"("m"_1"m"_2)/"d"^2`
Simplify the following:
`2 "log" 5 +"log" 8 - (1)/(2) "log" 4`
If log 16 = a, log 9 = b and log 5 = c, evaluate the following in terms of a, b, c: `"log"2(1)/(4)`
If 2 log x + 1 = 40, find: x
If 2 log x + 1 = 40, find: log 5x
If log 27 = 1.431, find the value of the following: log 9
If x2 + y2 = 7xy, prove that `"log"((x - y)/3) = (1)/(2)` (log x + log y)
