Question

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


x = −9

x = −3

x = 0

x = 4

Answer 1

We can make the base of the equation same on both the sides and then equate the exponents to get the answer as shown below:

$(\sqrt{6})^{8x}=(216)^{x-3} \\ \\ (\sqrt{6})^{8x}=(6^{3})^{x-3} \\ \\ (6^{\frac{1}{2}}) ^{8x}=(6)^{3x-9} \\ \\ (6)^{4x} =(6)^{3x-9} \\ \\ 4x=3x-9\\ \\ 4x-3x=-9\\ \\ x=-9$

Therefore, first option gives the correct answer