Math, asked by pranshul6, 1 year ago

If 2^x = 4^y = 8^z and 1/2x+1/4y+1/6z=24/7

then the value of z is:


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Answers

Answered by madeducators4
53

Given :

2^{x} =4^{y} = 8^{z}                 - (1)

\frac{1}{2x} + \frac{1}{4y} + \frac{1}{6z} =\frac{24}{7}         - (2)

To Find :

Value of z = ?

Solution :

From eq (1) :

2^{x} = (2^{2}) ^{y}   = (2^{3}) ^{z} \\

2^{x}  = 2^{2y}  = 2^{3z}

x = 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}

3\times \frac{1}{6z} =\frac{24}{7}

2z=\frac{7}{24}

z=\frac{7}{48}

So finally the value of z is  \frac{7}{48} .

Answered by aarav3103
3

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

.

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