If $27^{x + 1} = 9^{x + 3} = 3^{y}$ , then $x$ and $y$ are

3, 12

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

12, 3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

6, 6

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $3, 12$
$27^{x + 1} = 9^{x + 3}$
$\Rightarrow (3^{3})^{x + 1} = (3^{2})^{x + 3}$
$\Rightarrow 3^{3 x + 3} = 3^{2 x + 6}$
$\Rightarrow 3 x + 3 = 2 x + 6$
$\Rightarrow 3 x - 2 x = 6 - 3$
$\Rightarrow x = 3$
Consider $9^{x + 3} = 3^{y}$
$\Rightarrow (3^{2})^{x + 3} = 3^{y}$
$\Rightarrow 3^{2 x + 6} = 3^{y}$
$\Rightarrow 2 x + 6 = y$
$∴ 2 (3) + 6 = y = 12$

Suggest Corrections

Similar questions

x, y .

27^{x + 1} = 9^{x + 3} = 3^{y}

27^{x + 1} = 9^{x + 3} = 3^{y}

x

y

if x>0 and x^2+1/9x^2 =25/36, find:x^3+1/27x^3.

\frac{27 x^{3} y}{9 x^{2}} =

α, β

x^{2} - 3 x + a = 0

γ, δ

x^{2} - 12 x + b = 0

α, β, γ, δ

Join BYJU'S Learning Program