Advertisements
Advertisements
प्रश्न
If a2 = log x, b3 = log y and 3a2 - 2b3 = 6 log z, express y in terms of x and z .
Advertisements
उत्तर
Given that
a2 = log x, b3 = log y and 3a2 - 2b3 = 6 log z
Consider the equation,
3a2 - 2b3 = 6log z
⇒ 3log x - 2log y = 6log z
⇒ logx3 - logy2 = logz6
⇒ log `(x^3/y^2)` = logz6
⇒ `x^3/y^2 = z^6`
⇒ `x^3/z^6 = y^2`
⇒ `y^2 = x^3/z^6`
⇒ y = `( x^3/z^6 )^(1/2)`
⇒ y = `( x^(3/2)/z^(6/2))`
⇒ y = `x^(3/2)/z^3`
APPEARS IN
संबंधित प्रश्न
If a2 + b2 = 23ab, show that:
log `(a + b)/5 = 1/2`(log a + log b).
If m = log 20 and n = log 25, find the value of x, so that :
2 log (x - 4) = 2 m - n.
Find x, if : logx (5x - 6) = 2
Given log10x = 2a and log10y = `b/2`. Write 10a in terms of x.
Solve the following:
log (3 - x) - log (x - 3) = 1
Solve the following:
log 4 x + log 4 (x-6) = 2
Solve the following:
`log_2x + log_4x + log_16x = (21)/(4)`
If `"log" x^2 - "log"sqrt(y)` = 1, express y in terms of x. Hence find y when x = 2.
If 2 log x + 1 = log 360, find: log (3 x2 - 8)
Express the following in a form free from logarithm:
`2"log" x + 1/2"log" y` = 1
