Question

if 2^x=3^y=6^y show that 1/x+1/y=1/z​

Answer 1

Answer:

$2^{x} = 3^{y} = 6^{-z} =k2x=3y=6−z=k </p><p></p><p>Then:</p><p></p><p>2 = k^{ \frac{1}{x}}2=kx1 </p><p></p><p>3=k^{ \frac{1}{y}}3=ky1 </p><p></p><p>6 = k^{- \frac{1}{z}}6=k−z1 </p><p></p><p>We know that,</p><p></p><p>i) 3 × 2 = 6</p><p></p><p>ii) xᵃ × xᵇ = xᵃ⁺ᵇ</p><p></p><p></p><p>Then,</p><p></p><p>3 \times 2 = 63×2=6 </p><p></p><p>Now, Substitute value of 3, 2,& 6.</p><p></p><p>k^{ \frac{1}{x}} \times k ^{ \frac{1}{y}} = k^{- \frac{1}{z}}kx1×ky1=k−z1 </p><p></p><p>The bases are equal . </p><p></p><p>So,$

$So,</p><p></p><p>→ \frac{1}{x} + \frac{1}{y} = - \frac{1}{z}x1+y1=−z1 </p><p></p><p>→ \frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 0x1+y1+z1=0 </p><p></p><p>Hence proved.</p><p>_____________________________________________-</p><p></p><p>Hope my answer is helpful to you.</p><p>$