Advertisements
Advertisements
Question
Prove that: `(1)/("log"_8 36) + (1)/("log"_9 36) + (1)/("log"_18 36)` = 2
Advertisements
Solution
L.H.S.
= `(1)/("log"_8 36) + (1)/("log"_9 36) + (1)/("log"_18 36)`
= log36 8 + log36 9 + log36 18
= `("log"8)/("log"36) + ("log"9)/("log"36) + ("log"18)/("log"36)`
= `(1)/("log"36)("log" 8 + "log"9 + "log"18)`
= `(1)/("log"36)("log"2^3 + "log"3^2 + "log"(2 xx 3^2))`
= `(1)/("log"(2^2 xx 3^2))("log"2^3 + "log"3^2 + "log"2 + "log"3^2)`
= `(1)/("log"(2^2 xx 3^2))(3"log"2 + 2"log"3 + "log"2 + "log"3)`
= `(1)/(2"log"2 + 2"log"3)(4"log"2 + 4"log"3)`
= `(4)/(2("log"2 + "log"3))("log"2 + "log"3)`
= 2
= R.H.S.
Hence proved.
APPEARS IN
RELATED QUESTIONS
If a2 + b2 = 23ab, show that:
log `(a + b)/5 = 1/2`(log a + log b).
Solve the following:
log 7 + log (3x - 2) = log (x + 3) + 1
Solve for x: `("log"125)/("log"5)` = logx
Solve for x: `("log"289)/("log"17)` = logx
State, true of false:
If `("log"49)/("log"7)` = log y, then y = 100.
If log 3 m = x and log 3 n = y, write down
32x-3 in terms of m
Find x and y, if `("log"x)/("log"5) = ("log"36)/("log"6) = ("log"64)/("log"y)`
If a = `"log" 3/5, "b" = "log" 5/4 and "c" = 2 "log" sqrt(3/4`, prove that 5a+b-c = 1
Express the following in a form free from logarithm:
m log x - n log y = 2 log 5
If `"a" = "log""p"^2/"qr", "b" = "log""q"^2/"rp", "c" = "log""r"^2/"pq"`, find the value of a + b + c.
