Question

If 1, log, x, log, y,-15 log, z are in A.P., then
(a) 2) = x
(b)x=y-1
(c) 2-3 = y
(d) all of these​

Answer 1

Answer:

Step-by-step explanation:

Given 1, logy x, logz y, -15 logx z are in A. P.

Let the common difference be d.

logy x – 1 = d

logy x = 1+d

x = y1+d …(i)

logz y = 1+2d

y = z1+2d …(ii)

-15 logx z = 1+3d

z = x-(1+3d)/15 …(iii)

x = y1+d = z(1+2d)(1+d) = x-(1+d)(1+2d)(1+3d)/15

Comparing powers of x

(1+d)(1+2d)(1+3d) = -15

(2d2+3d+1)(3d+1) = -15

6d3+11d2+6d+16 = 0

(d+2)(6d2-d+8) = 0

=> d = -2

Therefore, x=z^3