If 2^(x) = 4^(y) = 8^(z) and 1/(2x) + 1/(4y) + 1/(4z) = 4 then the value of x is

Pragati Rode   9 years AGO

2^(x) = 4^(y) =8^(z)
convert all base in same variable
from this equation, we get 2^(x) = 2^(2x) = 2^(3x)
y =x/2 and z=x/3
put this value in second equation, we get
1/2x + 1/(4*x/2) + 1/(4*x/3)=4

1/2x + 1/2x + 3/4x = 4
by solving this we get, 7 = 16x
x = 7/16
so answer is option 10)

Like? Yes (43) | No (15)  

Yadu Vir Singh   9 years AGO

Given:- 2^x = 4^y = 8^z
=> 2^(x) = 2^(2 y) = 2^(3 z)
So, => x = 2 y = 3 z
Putting these values in 2nd equation, it will be:-
1/(2 x) + 1/(2 x) + 3/(4 x) = 4
16 x = 7
x = 7/16

Like? Yes (40) | No (23)  

Rama lakshmi   9 years AGO

2^(x)=4^(y)=8^(z)
So x=2y=3z;
1/(2x)+1/(4y)+1/(4z)=7/(4x)=4
x=7/16

Like? Yes (17) | No (8)  

THOWSIF   9 years AGO

2^(x)=2^(2y)=2^(3z)
x=2y=3z
1/2x + 1/4(x/2) + 1/4(x/3)
x=7/16

Like? Yes (13) | No (7)  

Suraj Mishra   9 years AGO

2^x =4^y=8^z
taking log
x(log(2)=2y(log(2)=3z(log(2)
and log will cancel out
so x=2y=3z
puting this value in 2nd equation
1/(2x)+ 1/2x+ 3/4x= 4
which gives x=7/16

Like? Yes (8) | No (6)  

SHUBHAM   9 years AGO

using property of log,we get the equation
xlog2=2ylog2=3xlog2
thus X=2y=3z
and now this we get after substituting,X=7/16

Like? Yes (6) | No (5)  

Pooja Shaw   9 years AGO

2^(x)=4^(y)=8^(z)
2^x=2^(2y)=2^(3z)
x=2y=3z
y=x/2 z=x/3
1/2x+1/4x+1/4z=4
1/2x+1/2x+3/4x=4 (putting the value of y,z)
(2+2+3)/4x=4
7=16x
x=7/16
thus,correct option is 10)7/16

Like? Yes (3) | No (2)  

MRITUNJAY   9 years AGO

2^x=2^2y=2^3z

x=2y=3z=k

x=k,y=k/2,z=k/3
1/2k+1/4*k/2+1/4*k/3=4

k=7/16

x=7/16

Like? Yes (3) | No (3)  

ABHINAV PUSHPAM   9 years AGO

2^(x) = 4^(y) = 8^(z)
or, 2^(x) = 2^(2y) = 2^(3z)
x = 2y = 3z
therefore, 1/(2x) + 1/(4y) + 1/(4z) =4
1/(2x)+ 1/(2*2y) + 1/(4/3*3z) =4
1/2x + 1/2x + 1/(4/3x) = 4
so, X= 7/16
option (10) is correct.

Like? Yes (6) | No (6)  

anuradha   9 years AGO

since equating powers from first condition we get, x=2y=3z
substituting the value of x in second condition, we get 7/16

Like? Yes (2) | No (2)  

Jamil Ahmed   9 years AGO

2^(x)=4^(y)=8^(z)
Therefore, x=2y=3z.

By putting the values of y & z in 1/2x +1/4y + 1/4z = 4,
we get 1/2x + 1/2x + 3/4x = 4
or 7/4x = 4
Therefore, x = 7/16.

Like? Yes (2) | No (2)  

Deepak kumar singh   9 years AGO

2^x=2^2y=2^3z => x=2y=3z
=>1/2x+2/4 x+3/4x=4
=>x=7/16

Like? Yes (1) | No (1)  

Ritesh kumar   9 years AGO

ans=7/16
2^x=4^y, 2^x=8^z
log2^x=log4^y , log2^x=log8^z
xlog2=ylog4 , xlog2=zlog8
on solving this
x=2y, x=3z
put in the eq..
and then found x= 7/16

Like? Yes (4) | No (4)  

Venkateswarlu   9 years AGO

from the first equation==>x=2y=3z;
y=x/2;z=x/3;
(1/2x)+(2/4x)+(3/4x)=4 ==> (1/x)+(3/4x)=4
(4+3/4x)=4 ==> 7=16x ==> x=7/16.

Like? Yes (5) | No (5)  

CHANDAN KUMAR   9 years AGO

given
2^x=2^2y =2^3z

so,
x=2y=3z..... (I)

now,
1/2x + 1/4y +1/4z =4
solving we get,
z= 7/48

but
x =3z =3×7/48 = 7/16
correct options are 10) 7/16

Like? Yes (2) | No (2)  

RAHUL KUMAR   9 years AGO

2^(x) = 4^(y) = 8^(z)
or, 2^(x) = 2^(2y) = 2^(3z)
x = 2y = 3z
therefore, 1/(2x) + 1/(4y) + 1/(4z) =4
1/(2x)+ 1/(2*2y) + 1/(4/3*3z) =4
1/2x + 1/2x + 1/(4/3x) = 4
so, X= 7/16
option (10) is correct.

Like? Yes (5) | No (6)  

T Purushotham   9 years AGO

by x=2y,x=3z replacing in the euation we get x=7/16
1/2x+1/4*(x/2)+1/4*(x/3)=4;
x=7/16

Like? Yes (3) | No (4)  

Devendra Marghade   9 years AGO

2^(x)=4^(y)=2^(2*y), x=2y or y=x/2 and
2^(x)=8^(z)=2^(3*z), x=3z or z=x/3
Given 1/(2x)+1/(4y)+1/(4z)=4
So substituting values of y, z in terms of x we get
1/(2x) + 2/(4x) + 3/(4x) =4
7/4x=4, x=7/16
Option 10)

Like? Yes (2) | No (3)  

Nandkishor jaiswal   9 years AGO

given that
2^x=4^y=8^z
so x=2*y=3*z
from equation 1/2x+1/4y+1/4z=4
x=7/16

Like? Yes (1) | No (2)  

teja srinivas   9 years AGO

2^(x)=4^(y)=8^(z)
this will become x=2y=3z
by simplification
x=7/16

Like? Yes (1) | No (2)  

vamsi krishna   9 years AGO

we got x=2y=3z
y=x/2, z=x/3
1/2x + 1/2x + 3/4x = 4
7/4x = 4
x = 7/16

Like? Yes (2) | No (3)  

REYAZ FAHIM ANSARI   9 years AGO

2^x =4^y=8^z by taking log we get x=2y, 2y=3z, x=3z
after putting the values of y & z in terms of x we get,
x= 7/16

Like? Yes (1) | No (2)  

SHIVAM KUMAR KAUSHIK   9 years AGO

2^x=2^2y=2^3z
x=2y=3z
put the vaule in given equation,
1/2x +2/4x +3/4x =4
x=7/16

Like? Yes (1) | No (2)  

TARUN CHAUHAN   9 years AGO

2^x=8^z
taking log z=x/3
similarly y=x/2

put it in eq. we get
1/2x+1/2x+3/4x=4

x=7/16

Like? Yes (1) | No (2)  

vishal varma   9 years AGO

here from given equation we get x=2y=3z
from that y=x/2 ; z=x/3
substitute these values in equation 2 and by soving we get
x=7/16

Like? Yes (2) | No (4)  

chetan   9 years AGO

From 1st condition we get x=2y=3z.
From 2nd condition we get 2yz+xz+xy=16xyz.
2yz+2yz+3yz=16xyz
=> x=7/16.
So option 10 is correct.

Like? Yes (2) | No (4)  

armaan   9 years AGO

x=2y=3z
then palce all the value of x,y and z in the given quation..where we find 7/16

Like? Yes (1) | No (3)  

PRABHAT KUMAR   9 years AGO

2^x=2^2y=2^3z
x=2y=3z=k
x:y:z=6k=3k=2k
Putting value in given equation we can get value of k
1/12k+1/12k+1/8k=4
k=7/96
Therefore x=6k=6*(7/96)=7/16
Option 10

Like? Yes (1) | No (4)  

harshavi   9 years AGO

2^(x)=2^(2y)=2^(3y)
therefore x=2y=3z
thus by substituting we get
(1/2x)+(1/2x)+(3/4x)=4
(7/4x)=4
x=7/16

Like? Yes (1) | No (4)  

Nimish   9 years AGO

when bases are same powers are equal Therefore 2^x=2^2y=2^3z
evaluate x in terms of y and x in terms of z put in 2nd equation and solve it

Like? Yes (1) | No (5)