Question

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

Answer 1

-9

Explanation:

`(√(6)) ^8^(x) = 216^x^(-3)`

step one: create equal bases

`6^(1/2) (^8^(x) )`

`6^3 =216`

so it would be

`6^(1/2) (^8^(x) ) = (6^3)^x^(-3)`

`6^(4x) = (6^3)^(3x-9)`

the bases cancel out leaving:

`4x=3x-9`

Step 2: Solve for the variable

`4x=3x-9`

subtract 3x from each side

leaving x = -9

Answer 2

x = 6.0139

Explanation:

1) think of the first side of the equation as: 6^(8/2) - simplify by dividing the 8 by 2 to get 6^4.

2) The Equation now is 6^4 = 216x - 3, turn 6^4 into 1296 and add 3 to both sides to get 1299 = 216x.

3)Divide both sides by 216 to get x = 6.0139 (which is approximately close to 6 but technically plugging the answer into the equation in step 2 would yield 1296 = 1296).