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
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(3)(144)`
Express the following in terms of log 2 and log 3: `"log"root(5)(216)`
Express the following in terms of log 2 and log 3: `"log" root(4)(648)`
Write the logarithmic equation for:
V = `(1)/("D"l) sqrt("T"/(pi"r")`
Express the following as a single logarithm:
log 18 + log 25 - log 30
Express the following as a single logarithm:
`2 "log" 3 - (1)/(2) "log" 16 + "log" 12`
If log a = p and log b = q, express `"a"^3/"b"^2` in terms of p and q.
If x2 + y2 = 6xy, prove that `"log"((x - y)/2) = (1)/(2)` (log x + log y)
Simplify: log b ÷ log b2
