Advertisements
Advertisements
Question
Express the following as a single logarithm:
`2"log"(9)/(5) - 3"log"(3)/(5) + "log"(16)/(20)`
Advertisements
Solution
`2"log"(9)/(5) - 3"log"(3)/(5) + "log"(16)/(20)`
= 2log9 - 2log5 - 3log3 + 3log5 + log16 - log20
= 2log(32) - 2log5 - 3log3 + 3log5 + log(42) - log(5 x 4)
= 4log3 - 2log5 - 3log3 + 3log5 + 2log4 - log5 - log4
= (4 - 3)log3 + (-2-1+3)log5 + log4
= log3 + log4
= log(3 x 4)
= log12.
APPEARS IN
RELATED QUESTIONS
If log (a + b) = log a + log b, find a in terms of b.
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: log250
Write the logarithmic equation for:
V = `(1)/("D"l) sqrt("T"/(pi"r")`
Express the following as a single logarithm:
`(1)/(2)"log"25 - 2"log"3 + "log"36`
Simplify the following:
`2 "log" 5 +"log" 8 - (1)/(2) "log" 4`
If log 2 = 0.3010, log 3 = 0.4771 and log 5 = 0.6990, find the values of: `"log" sqrt(72)`
If x2 + y2 = 6xy, prove that `"log"((x - y)/2) = (1)/(2)` (log x + log y)
If x2 + y2 = 7xy, prove that `"log"((x - y)/3) = (1)/(2)` (log x + log y)
Simplify: log b ÷ log b2
