3 to the power of 2 times 3 to the power of x equals 3 to the power of 7

3 to the power of 2 times 3 to the power of x equals 3 to the power of 7.

Write this out:
3^2 * 3^x = 3^7

When we multiply matching coefficients, we add exponents, so we have:
3^(2 + x) = 3^7

Therefore, 2 + x = 7. To solve this equation for x, we type it into our search engine and we get:
x = 5