Question

Solve open parentheses square root of 6 close parentheses to the 8 x power = 216x−3.

Answer 1

We are seeking to get the value of x.

We will use the concept of indices.

1. When two numbers that are equal and have same bases ,their powers are also equal.

Let's write this question in form of an eqaution:

We have :

( √6 )⁸ˣ = 216⁽ˣ ⁻³⁾

√6 = 6∧ 1/2

(6∧1/2)⁸ˣ = 6⁴ˣ

216 = 6³

216⁽ˣ ⁻³⁾ = 6³ˣ ⁻⁹

6³ˣ⁻⁹ = 6⁴ˣ

Since the bases are equal the powers are also equal.

3x - 9 = 4x

4x - 3x = -9

x = -9