Advertisements
Advertisements
Question
If `"log" x^2 - "log"sqrt(y)` = 1, express y in terms of x. Hence find y when x = 2.
Advertisements
Solution
`"log" x^2 - "log"sqrt(y)` = 1
⇒ `"log"(x^2/sqrt(y))` = log 10
⇒ `x^2/sqrt(y)` = 10
⇒ `sqrt(y) = x^2/(10)`
Squaring both sides, we get
y = `(x^2/10)^2 = x^4/(100)`
Now, when x = 2,
y = `(2^4)/(100) = (16)/(100) = (4)/(25)`.
APPEARS IN
RELATED QUESTIONS
If a2 + b2 = 23ab, show that:
log `(a + b)/5 = 1/2`(log a + log b).
If log2(x + y) = log3(x - y) = `log 25/log 0.2`, find the values of x and y.
Given : `log x/ log y = 3/2` and log (xy) = 5; find the value of x and y.
Given log10x = 2a and log10y = `b/2`. Write 102b + 1 in terms of y.
If 2 log x + 1 = log 360, find: x
Express the following in a form free from logarithm:
m log x - n log y = 2 log 5
Express the following in a form free from logarithm:
`2"log" x + 1/2"log" y` = 1
Express the following in a form free from logarithm:
5 log m - 1 = 3 log n
If a b + b log a - 1 = 0, then prove that ba.ab = 10
Prove that: `(1)/("log"_8 36) + (1)/("log"_9 36) + (1)/("log"_18 36)` = 2
