Question

if 2 to the power x = 3 to the power y =12 to the power z,prove that x=2yz/y-z

Answer 1

Answer:

Step-by-step explanation

Let 2^x=3^y=12^z=k

I. e. 2^x=k means 2=k^(1/x)

Similarly, 3=k^(1/y) & 12=k^(1/z)

We know that

2^2 x 3 = 12

Substitute the values in terms of k we get,

k^(2/x) k^1/y = k^(1/z)

k^[ (2/x) + (1/y) ] = k^(1/z)

Equating powers on both sides, we get

2/x + 1/y= 1/z

2/x = 1/z - 1/y

2/x = (y-z) /zy

x/2 = zy/(y-z)

x = 2yz/(y-z)

Hence proved.

Answer 2

Step-by-step explanation:

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