If 2^x = 4^y = 8^z and 1/2x+1/4y+1/6z=24/7
then the value of z is:
Answers
Given :
- (1)
- (2)
To Find :
Value of z = ?
Solution :
From eq (1) :
⇒
Now using equation (2) and putting the values of x and y in terms of z :
⇒
So finally the value of z is .
Step-by-step explanation:
Given :
2^{x} =4^{y} = 8^{z}2
x
=4
y
=8
z
- (1)
\frac{1}{2x} + \frac{1}{4y} + \frac{1}{6z} =\frac{24}{7}
2x
1
+
4y
1
+
6z
1
=
7
24
- (2)
To Find :
Value of z = ?
Solution :
From eq (1) :
\begin{gathered}2^{x} = (2^{2}) ^{y} = (2^{3}) ^{z} \\\end{gathered}
2
x
=(2
2
)
y
=(2
3
)
z
2^{x} = 2^{2y} = 2^{3z}2
x
=2
2y
=2
3z
⇒x = 2y =3zx=2y=3z
Now using equation (2) and putting the values of x and y in terms of z :
\frac{1}{2 \times 3z} +\frac{1}{2 \times 3z} + \frac{1}{6z} = \frac{24}{7}
2×3z
1
+
2×3z
1
+
6z
1
=
7
24
3\times \frac{1}{6z} =\frac{24}{7}3×
6z
1
=
7
24
2z=\frac{7}{24}2z=
24
7
⇒z=\frac{7}{48}z=
48
7
So finally the value of z is \frac{7}{48}
48
7
.