Final answer:
To solve for x in the expression 6^9 × 6^x = 6^2, we use the product of powers property, which states that when multiplying powers with the same base, we add the exponents. Setting the exponents equal, we find that x = 2 - 9, so x = -7.
Step-by-step explanation:
To find the value of x in the expression 69 × 6x = 62, we can use the properties of exponents. According to the product of powers property, when we multiply powers with the same base, we add the exponents. Therefore, 69 × 6x can be expressed as 69+x. For this to equal 62, the exponents must be equal, meaning 9 + x = 2. Solving for x, we subtract 9 from both sides to get x = 2 - 9, which simplifies to x = -7.