Given, √(27^x+1)=9^x 2 Now squaring both sides we get, 3^(3x+3)=3^2× 2(x 2) or, 3x+3=4(x 2) or, 3x+3=4x 8 or, x=11 . ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Estimating the Square Root

Solve: √27x+...

Question

Solve: $\sqrt{27^{x + 1}} = 9^{x - 2}$

Open in App

Solution

Given,
$\sqrt{27^{x + 1}} = 9^{x - 2}$
Now squaring both sides we get,
$3^{(3 x + 3)} = 3^{2 \times 2 (x - 2)}$
or, $3 x + 3 = 4 (x - 2)$
or, $3 x + 3 = 4 x - 8$
or, $x = 11$ .

Suggest Corrections

Similar questions

x : 9 x^{4} - 27 x^{2} - 36 = 0

x^{9}

(1 + 9 x + 27 x^{2} + 27 x^{3})^{6}

y^{3} - 9 x^{2} + 27 x - 27 = 0 z^{3} - 9 y^{2} + 27 y - 27 = 0 x^{3} - 9 z^{2} + 27 z - 27 = 0

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

\frac{sin x}{cos 3 x} + \frac{sin 3 x}{cos 9 x} + \frac{sin 9 x}{cos 27 x} = \frac{1}{2} [tan 27 x - tan x]

Join BYJU'S Learning Program