Question

Prove that 2 power x + 1 is equals to 3 power 1 - x

Answer 1

Answer:

Let:

2^{x} = 3^{y} = 6^{-z} =k

Then:

2 = k^{ \frac{1}{x}}


3=k^{ \frac{1}{y}}

6 = k^{- \frac{1}{z}}

We know that,

i) 3 × 2 = 6

ii) xᵃ × xᵇ = xᵃ⁺ᵇ

Then,

3 \times 2 = 6

Now, Substitute value of 3, 2,& 6.

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

The bases are equal .

So,

→ \frac{1}{x} + \frac{1}{y} = - \frac{1}{z}

→ \frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 0

Hence proved.