Question

Find the value of x 9^3 x+2=27^x-2

Answer 1

Answer:

The value of x in the following is $\frac{-10}{3}$

Step-by-step explanation:

In the given equation we have,

$9^{3x + 2} = 27^{x-2}$

For solving this we will first make the bases of both sides similar.

We know that 27 = $3^{3}$ and also 9 =$3^{2}$ therefore we put the following value in the expression above,

⇒$3^{2(3x+2)} = 3^{3(x-2)}$

⇒$3^{6x +4} = 3^{3x-6}$

∴6x + 4 = 3x - 6

⇒ 6x - 3x = -6 -4

⇒ 3x = -10

⇒x = $\frac{-10}{3}$

Therefore the answer or the value of x = $\frac{-10}{3}$