3root32 = 8^3x * 2^6x

Answer 1

To solve for x, we need to simplify both sides of the equation.

On the left side: 3√32 = 3√(2^5) = 2^(5/3)

On the right side: 8^3x * 2^6x = (2^3)^3x * 2^6x = 2^(9x) * 2^(6x) = 2^(15x)

So the equation becomes: 2^(5/3) = 2^(15x)

Since the bases are the same, we can set the exponents equal to each other:

5/3 = 15x

Now, solve for x:

5/3 = 15x
x = 5/45
x = 1/9

Therefore, x = 1/9 is the solution to the equation.