Question

if 4x=5y=20z then z is equal to​

Answer 1

Answer: hello

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Answer 2

Answer:

The equation $4^{x} = 5^{y} = 20^{z}$ ,z is equal to $z = \frac{xy}{x +y}$

Step-by-step explanation:

Given: The equation $4^{x} = 5^{y} = 20^{z}$

To find: The value of z

Solution:

Given that $4^{x} = 5^{y} = 20^{z}$

Let us take,

$4^{x} = 5^{y} = 20^{z} =k$

$4^{x} = k$

Now take log on both sides then we get,

x log4 = log k

x = $\frac{log k}{log 4}$

$5^{y} = k$

Now take log on both sides then we get,

y log 5 = log k

y = $\frac{log k}{log 5}$

$20^{z} = k$

Now take log on both sides we get

z log 20 = k

z = $\frac{log k}{log 20}$

z = $\frac{log k}{log (5 * 4)}$

z = $\frac{log k}{log 5 + log 4}$

Now,

$\frac{1}{x} + \frac{1}{y} = \frac{log 4}{log k} + \frac{log 5}{log k}$

    = $\frac{log 4 + log 5}{log k}$

= $\frac{log(4*5)}{log k}$

= $\frac{log (20)}{k}$

 = $\frac{1}{z}$

$\frac{1}{x} + \frac{1}{y} = \frac{1}{z}$

$\frac{x+y}{xy} = \frac{1}{z}$

$z = \frac{xy}{x +y}$

Final answer:

The value of z is $\frac{xy}{x +y}$

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