olve the radical equation.

Question

3
⋅
2
(
x
−
6
)
5
=
6
3⋅
5

2(x−6)
​
=6

Answer 1

To solve the equation

\[ 3 \cdot 2(x - 6)^5 = 6, \]

first, we can simplify the equation by dividing both sides by 3:

\[ 2(x - 6)^5 = 2. \]

Next, divide both sides by 2:

\[ (x - 6)^5 = 1. \]

Now, take the fifth root of both sides:

\[ x - 6 = 1. \]

Finally, add 6 to both sides to solve for \( x \):

\[ x = 1 + 6 = 7. \]

Thus, the solution to the equation is

\[ \boxed{7}. \]