|

Mathematics

If 3^{x + 1} = 9^{x - 3}, find the value of 2^{1 + x}.

Indices

2 Likes

Answer

Given,

⇒ 3^{x + 1} = 9^{x - 3}

⇒ 3^{x + 1} = (3²)^{x - 3}

⇒ 3^{x + 1} = 3^{2(x - 3)}

⇒ 3^{x + 1} = 3^{2x - 6}

⇒ x + 1 = 2x - 6

⇒ 2x - x = 1 + 6

⇒ x = 7.

Substituting value of x in 2^{1 + x}, we get :

⇒ 2^{1 + 7} = 2⁸ = 256.

Hence, 2^{1 + x} = 256.

Answered By

1 Like

Related Questions

Solve :
3^{x - 1} × 5^{2y - 3} = 225
View Answer

If $\Big(\dfrac{a^{-1}b^2}{a^2b^{-4}}\Big)^7 ÷ \Big(\dfrac{a^3b^{-5}}{a^{-2}b^3}\Big)^{-5} = a^x.b^y$ , find x + y.
View Answer
If 2^x = 4^y = 8^z and $\dfrac{1}{2x} + \dfrac{1}{4y} + \dfrac{1}{8z}$ = 4, find the value of x.
View Answer
If $\dfrac{9^n.3^2.3^n - (27)^n}{(3^m.2)^3} = 3^{-3}$ .
Show that : m - n = 1.
View Answer