math problem?

Question

solve each equations

3^x3 = 9^x

can you explain how you solve this?

yes I mean

3^(x^3) = 9^x?

Answer 1

May I assume you mean 3^(x³) = 9^x?

If so, the first step is to match bases on the right side:

3^(x³) = (3²)^x
3^(x³) = 3^(2x)

Next, take the logarithm, base 3, of both sides to obtain:

x³ = 2x

Now this is just a polynomial equation, which may be easily solved:

x³ - 2x = 0
(x-√2)(x+√2)x = 0
x=-√2 or x=√2 or x=0.

And we are done.

Answer 2

Trivial.... x = 0. Do you mean 3^(x^3) = 9^x?