Advertisements
Advertisements
Question
Express the following in terms of log 2 and log 3: `"log" root(4)(648)`
Advertisements
Solution
`"log" root(4)(648)`
= `"log"(648)^(1/4)`
= `(1)/(4)"log"648`
= `(1)/(4)"log"(2^3 xx 3^4)`
= `(1)/(4)"log"2^3 + (1)/(4)"log"3^4`
= `(3)/(4)"log"2 + (4)/(4)"log3`
= `(3)/(4)"log"2 + "log"3`.
APPEARS IN
RELATED QUESTIONS
If log10 a = b, find 103b - 2 in terms of a.
If log5 x = y, find 52y+ 3 in terms of x.
Express the following in terms of log 2 and log 3: `"log"root(5)(216)`
Express the following as a single logarithm:
log 144 - log 72 + log 150 - log 50
Express the following as a single logarithm:
`2 "log" 3 - (1)/(2) "log" 16 + "log" 12`
Express the following as a single logarithm:
`2"log"(9)/(5) - 3"log"(3)/(5) + "log"(16)/(20)`
If log a = p and log b = q, express `"a"^3/"b"^2` in terms of p and q.
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 2 log y - log x - 3 = 0, express x in terms of y.
Find the value of:
`("log"sqrt(27) + "log"8 + "log"sqrt(1000))/("log"120)`
