Final answer:
To calculate the value of x in the equation 4²ˣ × 3ˣ = 6, you can simplify the left side of the equation by using the product rule of exponents. Then, you can solve for x by taking the logarithm of both sides with base 48.
Step-by-step explanation:
To calculate the value of x in the equation 4²ˣ × 3ˣ = 6, we can start by simplifying the left side of the equation. 4²ˣ can be written as (4²)ˣ, which is equal to (16)ˣ. Similarly, 3ˣ remains the same. Now, we can combine the two exponential terms by using the product rule of exponents, which states that (aˣ)(aʸ) = aˣ⁺ʸ. So, (16)ˣ × 3ˣ is equal to (16 × 3)ˣ. Therefore, we have (48)ˣ = 6. To solve for x, we can take the logarithm of both sides with base 48, which gives us log₄₈(48)ˣ = log₄₈(6). Since log₄₈(48) = 1, we have 1ˣ = log₄₈(6), and thus x = log₄₈(6).