Question

solve this mate plzz ​

Answer 1

Answer:

Step-by-step explanation:

ANSWER:-

Given that:-

$\sf{2^x=3^y=12^z}$, every number is equal to other number.

So ,

$\sf{2^x = k [considered]}$, so when we will transfer the power,

$\sf{2 = k^{\frac{1}{x}}$_________________________________(1)

Similarly, with the second one,

$\sf{3^y = k} \ [considered]$,

$\sf{3 = k^{\frac{1}{y}}$,__________________________________(2)

And

$\sf{12^z = k$

$\sf{12 = k^{\frac{1}{z}$______________________(3)

We now need to bring 12 in the base of 2 and 3.

So we know that:-

$\sf{2 \times 2\times 3 = 12}$

Again we got the values,

Now we will just replace the equations (1) and (2) and (3), we get

$\sf{k ^{\frac{1}{x} } \times k^{\frac{1}{x}} \times k^{\frac{1}{y}} = k^{\frac{1}{z}}$

We know that

• same bases, multiplication happens
• And also, equated due to same bases.

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

$\sf{\frac{2}{x}+\frac{1}{y}=\frac{1}{z}}$

$\sf{\frac{2}{x}= \frac{1}{z}-\frac{1}{y}}$

$\sf{\frac{2}{x} = \frac{y-z}{yz}}$

$\sf{\frac{1}{x} = \frac{y-z}{2yz}}$

$\sf{x = \frac{2yz}{y-z}}$

Hence Proved!

Answer 2

Answer:

find the value of lambda if mode of the data is 20: 15, 20, 25, 18,13, 15, 25,15, 18, 17,20,25,20 lambda 18 by subtracting.