math
posted by Shobhit
If a^x=b^y=c^z and b^2=ac then find value of y.

Steve
a^(xyz) = b^(y^2z)
c^(xyz) = b^(xy^2)
(ac)^(xyz) = b^(xy^2+y^2z)
but, ac = b^2, so
(ac)^(xyz) = (b^2)^(xyz) = b^(2xyz)
so,
xy^2 + y^2z = 2xyz
y^2(x+z)  2xyz = 0
y((x+z)y2xz) = 0
so, y=0 or y=2xz/(x+z)
or, from a different angle, since a = b^2/c,
(b^2/c)^x = b^y
xln(b^2/c) = y lnb
y = xln(b^2/c)/lnb
b^y = (b^2/a)^z
y lnb = z ln(b^2/a)
y = z ln(b^2/a)/lnb
pick some values for a,b,c: (2,4,8)
Then x = 3z
y = ln4/(z ln8)
or
y = ln4/(3z ln2)
y = 2xz/(x+z) = 6z^2/4z = 3z/2
so, if z=1, then x=3, y = 3/2
Respond to this Question
Similar Questions

math,help
I definately do not understand this problem. If y varies directly with x, and y = 600 when x = 1000, find the constant of variation K. If y is directonally (proportional) to x, then for every value of x there is a value for y multiplied … 
Math
Please help me I am terrible at math, and this is my last class before graduation.. 1. Find the value of X... x/6x/8=1 2. Find the value of X...x/x2x+1/x=8/x^22x 3. Find the value of X...5/x+6+2/x^2+7x+6=3/X+1 4.Find the value … 
math
Male: 60,63,65,70,66,80,85,73,79,80,83,85,81,76, 77,90,91,88,78,92 Females: 62,69,70,72,78,77,79,83,80,88,90,90,98,100, 66,67,65,63,69, 83 Can you hellp me I need to find: A) P value and the Z value of this data with a Alpha Value … 
Math
S is directly proportional to M^3. It is given that S=36 for a certain value of M. Find the value of S when this value of M is (a) doubled (b) reduced by 40% 
math
An initialvalue problem is given by the differential equation, f(x,y) = x + y, y(0) = 1.64 The Eulermidpoint method is used to find an approximate value to y(0.1) with a step size of h = 0.1. Then use the integrating factor method, … 
math
If y varies diretly with x, write an equation for the direct variation. then find each value. Find y when x = 10 if y = 8 when x = 20 If think I can find the value by y/10 = 8/20 with the answer for the value is 4. My problem is how … 
SAT Math
Can I please get some help on these questions: 1. If , find the value of 2 square root of 17x = 2x10, find the value of x/4. 2. If absolute value of 3x+6 < 9, then which of the following is a possible value of x ? 
Math
How to find coordinates of vertex, and find out if the function has minimum or maximum value and find that value? 
Math
1.What is the smallest possible value of 2x^4+(8/x^4) over all real nonzero values of x? 
math
if x is directy proportinal to y cube and y=2 when x= 1, (a) find an equation connecting x and y. (b) find the value of x when y = 1 (c) find the value of y when x=108.